The 34-year-old, bidding to become the oldest champion in New York in 45 years, took just 87 minutes to beat Gasquet for the 15th time in 17 meetings, his 6-3, 6-3, 6-1 victory only revealing half the story.
The Swiss fired 50 winners and 16 aces and did not face a single break point.
Federer hasn’t dropped a set at the tournament in five rounds and has been broken just twice.
But he will be wary of the danger posed by Wawrinka despite holding a 16-3 career edge.
Wawrinka defeated him in their last meeting in straight sets in the quarter-finals on his way to the French Open title in June.
“I faced the big serves of John Isner in the last round so I felt tonight I had a little extra time,” said second seed Federer.
“I stayed aggressive and enjoyed myself.”

Also enjoying themselves watching the master at work on Arthur Ashe Stadium were Andre Agassi and Bjorn Borg as well as celebrities such as Justin Timberlake and Bradley Cooper.
“Stan played wonderfully against me in Paris and I was happy for him that he won the title. He really deserved it,” added Federer, who was playing in his 46th Grand Slam quarer-final to Gasquet’s fourth.
“He has worked so hard and really improved. I am happy to play him here for the first time. It’s cool for us and Switzerland.”
Wawrinka reached the semi-finals with a 6-4, 6-4, 6-0 rout of South Africa’s Kevin Anderson.
Wawrinka, the 30-year-old fifth seed, booked a spot in his second US Open last-four match, having also reached the same stage in 2013.

“I played my best match of the tournament so far,” said Wawrinka.
“Against Roger, I will need to play my best to win. It’s a big challenege but I am ready.”
Anderson, the 15th seed and playing in his first Grand Slam quarter-final, had knocked out third seed Andy Murray in the previous round.
That effort seemed to take its toll as he committed 42 unforced errors and carved out just a single break point against the fifth-seeded Wawrinka, who romped to victory in just 107 minutes.
The result shattered 29-year-old Anderson’s hopes of becoming the first South African in the semi-finals in New York since Johan Kriek in 1980.

Anderson had won four of his last seven meetings with Wawrinka but he was horribly out of sorts on Wednesday, dropping serve in the seventh game of the first set and ninth of the second.
The third set was all over in 25 minutes with Anderson winning just five points.
“It was really tough out there. Was maybe a little bit nervous just with the occasion and a lot of waiting around, switching courts,” said Anderson after the match was moved from Ashe to Louis Armstrong Stadium because of worries over rain forecast for the evening.
“Obviously it’s something that you deal with, but just getting out there and everything seemed to be going pretty quickly.”

BJ Watling and Corey Anderson, however, shared an unbroken sixth-wicket partnership of 73 to give the touring side hope of saving the game and, chasing 345 for victory, they reached 134 for five at tea.
Anderson got to his fifty off 44 balls and was 51 not out at the interval with Watling unbeaten on 36.
Stokes, who struck the fastest test century at the home of cricket on Sunday, had the obdurate Williamson caught by Joe Root in the slips for 27 before bowling captain McCullum with a venomous delivery which cut back sharply.
Anderson survived the hat-trick ball and immediately went on the attack, hitting Stokes for two fours and a six, and he continued to play positively alongside the more circumspect Watling.
James Anderson and Stuart Broad ripped out the New Zealand top order to give England the scent of victory before lunch.
Martin Guptill edged Anderson’s second ball of the innings to Gary Ballance at third slip.
Broad trapped Tom Latham lbw with his first delivery to reduce the touring side to nought for two and then dismissed Ross Taylor in the same manner to leave New Zealand in tatters at 12 for three.
Williamson and Watling guided their side to the interval without further loss at 21 for three.
Earlier, New Zealand left-arm seamer Trent Boult picked up the last four wickets in under an hour to dismiss England for 478.
England resumed on 429 for six and Boult had captain Alastair Cook caught by wicketkeeper Latham for 162 before bowling Broad for 10.
Moeen Ali was lbw for 43 and Anderson was bowled for nought to give Boult figures of five for 85 and nine wickets in the match.

England 1st Innings 389
(J Root 98, B Stokes 92, J Buttler 67, M Ali 58; T Boult 4-79, M Henry 4-93)
New Zealand 1st Innings 523
(K Williamson 132, M Guptill 70, R Taylor 62, BJ Watling 61 no, T Latham 59; S Broad 3-77, M Wood 3-93, M Ali 3-94)
England 2nd Innings (overnight: 74-2)
A. Lyth c Southee b Boult 12
A. Cook c Latham b Boult 162
G. Ballance b Southee 00
I. Bell c Latham b Southee 29
J. Root c Boult b Henry 84
B. Stokes c Taylor b Craig 101
J. Buttler c Latham b Henry 14
M. Ali lbw b Boult 43

S. Broad b Boult 10
M. Wood not out 04
J. Anderson b Boult 00
Extras (b2, lb12, w5) 19
Total (all out, 129 overs, 571 mins) 478
Fall of wickets: 1-14, 2-25, 3-74, 4-232, 5-364, 6-389, 7-455, 8-467, 9-478
Bowling: Boult 34-8-85-5; Southee 34-4-162-2 (1w); Henry 29-3-106-2 (3w); Craig 28-3-96-1 (1w); Anderson 3-0-13-0; Williamson 1-0-2-0

New Zealand 2nd Innings (target: 345)

M. Guptill c Ballance b Anderson 00
T. Latham lbw b Broad 00
K. Williamson c Root b Stokes 27
R. Taylor lbw b Broad 08
B. Watling not out 36
B. McCullum b Stokes 00
C. Anderson not out 51
Extras (b-5 lb-7) 12
Total (for 5 wickets, 41 overs) 134
Fall of wickets: 1-0, 2-0, 3-12, 4-61, 5-61
Bowling : J. Anderson 9 – 5 – 11 – 1, S. Broad 11 – 3 – 28 – 2, M. Wood 8 – 2 – 20 – 0, B. Stokes 7 – 3 – 28 – 2, M. Ali 6 – 1 – 35 – 0