Federer, this year's runner-up to Rafael Nadal at the French Open, lost the previous two times he faced Tsonga, but he fought off an early rain delay and capitalized at the right time in his 30th straight Grand Slam quarterfinal.
"It doesn't matter straight sets or five sets. As long as you keep on progressing in a tournament and have a good time on the tennis court," Federer said. "That's what it's about. That's what I had tonight."
Federer, who made it to the semis for the eighth straight time in Flushing Meadows, won the final three games of the opening set, holding a love in the final game. That set was delayed by rain with Federer up 3-2.
He broke Tsonga twice quickly in the second and finished off that one when Tsonga sent a forehand return long.
The third was even after six games, but after holding serve Federer broke Tsonga when the Frenchman double-faulted, immediately after he fired a 139 mph serve that surprised his opponent.
Tsonga was able to save one match point, but then sent a backhand long, giving Federer a shot at his sixth U.S. Open title, which would be an Open era record. He currently shares the mark with Connors and Pete Sampras.
Sunny skies greeted the players earlier Thursday, as Djokovic reached the semifinals, while reigning champion Rafael Nadal and former champ Andy Roddick were among those posting fourth-round victories.
Rain wiped out all of the scheduled action on Tuesday, and only about 15 minutes of tennis was staged on Wednesday because of inclement weather at the USTA Billie Jean King National Tennis Center.
Because of the backlog of matches brought on by this week's rain, the men's final for Sunday has been rescheduled for Monday, which will mark the fourth straight Monday men's final at the Open. The quarterfinals will wrap up on Friday, while the semifinals, as originally scheduled, will be staged on Saturday.
On court Thursday, Djokovic improved to an incredible 62-2 this year with a 7-6 (7-2), 6-7 (3-7), 6-0, 3-0 victory over 20th-seeded good friend and fellow Serb Janko Tipsarevic at Ashe Stadium. An upset Tipsarevic, playing in his first career Grand Slam quarterfinal, retired in the fourth set with an apparent leg injury.
Djokovic, himself, had to address an injury on his left foot at the beginning of the fourth set, saying that it was bleeding after he slid on the court following a great forehand winner.
The 24-year-old star moved on in 3 hours, 27 minutes by breaking Tipsarevic eight times.
Djokovic has already tallied nine titles this year, including major wins at Wimbledon and the Australian Open. The super Serb was last year's U.S. Open runner-up to Nadal and lost to Federer in the 2007 finale in Flushing.
A second-seeded Nadal handled fellow left-hander Gilles Muller of Luxembourg 7-6 (7-1), 6-1, 6-2 at Ashe Stadium. The match was postponed on Tuesday and halted because of rain on Wednesday, with Muller leading 3-0 in the opening set.
Nadal moved on in 2 hours, 8 minutes, as Muller piled up 43 unforced errors and had his big serve broken six times by the fiery Spaniard.
The capable Muller stunned Nadal in a second-round affair at Wimbledon back in 2005, but Nadal avenged that defeat by besting Muller in the third round at Wimbledon 2011 earlier this summer.
The 10-time major champion Nadal is the reigning U.S. and French Open titlist.
Up next for him will be his fellow former world No. 1 Roddick.
"He's having one of the best careers, being in the top players for, I don't know, 11 years, 10 years, 9 years. That's a lot. That's amazing," Nadal said of Roddick. "So I have big respect for Andy, especially he's very tough to be there for a long time and he did."
A 21st-seeded Roddick held off fifth-seeded gritty Spaniard 6-3, 6-4, 3-6, 6-3 on a 584-seat Court 13.
Roddick-Ferrer commenced at Armstrong Stadium on Wednesday before rain halted play after about 15 minutes.
On Thursday, Roddick and Ferrer played two games before the American star complained that water was seeping up through a crack just beyond one of the baselines on the court at Armstrong. Following a lengthy delay in an attempt to fix the problem, the players were moved to an open court, which turned out to be the intimate Court 13.
Following the bizarre court change, Roddick would prevail in 2 hours, 39 minutes by swatting 19 aces and breaking Ferrer on four occasions. The Spaniard settled for 12 aces and two breaks in a losing effort.
"It's difficult for us, because, you know, two days raining; today it was not raining, but the court is not at good performance," a frustrated Ferrer said. "So it was not easy. But, you know, I can't do anything like this."
The USTA released a statement regarding the Armstrong court.
"We have faced an inordinate amount of rain in August and through the early part of September which has saturated the court surfaces at the USTA Billie Jean King National Tennis Center. All courts were completely dried prior to play on Thursday, September 8. However, as the sun began to warm, or "bake" the courts, evaporation of these saturated conditions began to surface on Louis Armstrong Stadium. Until this situation is rectified, no further play will occur on Louis Armstrong Stadium."
Roddick lost his cool with tournament referee Brian Earley during the court controversy at Armstrong.
"I was surprised the second time we got called out," Roddick said. "We walked back there and it was wet, so I couldn't quite figure out why we were called out. I even said it's coming from under. It's not something you can dab a towel on and make it go away. I watched the monitors, and they were dabbing towels on it the entire time. Then they called us back out, and we walked right over it and it was wet. I could not believe what I was looking at."
The 29-year-old Roddick captured his lone major title here in Flushing back in 2003 and was the runner-up here in 2006. He's 2-0 in his U.S. Open semifinal appearances.
Roddick will now meet Nadal for a 10th time, with the Spaniard leading the all-time series 6-3. The American topped Nadal in the second round at the 2004 U.S. Open.
Fourth-seeded 2008 U.S. Open runner-up Andy Murray flattened 22-year-old American Donald Young 6-2, 6-3, 6-3 on the Grandstand court. The match was suspended on Wednesday, with Young leading 2-1 in the first set. But the American was no match for the talented Brit on Day 11.
Murray, who closed out his Thursday exercise with a resounding ace, ultimately dismissed the overmatched Young in just under two hours, as the American littered the court with 53 unforced errors and had his serve broken a whopping eight times.
Young stunned Murray in the second round at an ATP Masters event at Indian Wells earlier this season.
The three-time Grand Slam runner-up Murray was this year's Aussie Open runner- up to Djokovic and lost to the great Federer in the 2008 U.S. Open finale.
Up next for Murray will be 6-foot-9 John Isner.
Roddick wasn't the only American to reach the quarters on Day 11, as a 28th- seeded Isner upended 12th-seeded Frenchman Gilles Simon 7-6 (7-2), 3-6, 7-6 (7-2), 7-6 (7-4) on Court 17. The towering American will now appear in his first career Grand Slam quarterfinal.
Isner advanced in 3 hours, 39 minutes by crushing 26 aces, which accounted for all of his winners on Day 11.
He was asked if this was the biggest win of his career.
"It's certainly one of them," Isner said. "I never made a Grand Slam quarterfinal before, so it's definitely up there. It feels good to get that one, you know, done with and over with."
The 26-year-old Isner is currently riding a nine-match winning streak, which includes a title in Winston-Salem in his native North Carolina.