Andy Murray and Stan Wawrinka were victorious on their US Open returns, while Kevin Anderson edged through a marathon clash.
Murray survived an early scare before claiming a four-set win over James Duckworth in the first round at Flushing Meadows on Monday.
Wawrinka, who like Murray missed the major last year, brushed past eighth seed Grigor Dimitrov.
Meanwhile, Anderson – the runner-up in 2017 – needed more than four hours to get through his opener.
MURRAY WANTS IMPROVEMENT DESPITE SOLID START
Back playing a grand slam for the first time since Wimbledon last year, Murray overcame Duckworth 6-7 (5-7) 6-3 7-5 6-3.
The Brit missed the major last year due to a hip injury and while he was upbeat, he is eager to get better.
"I actually felt like I could have moved better. I struggled a little bit with that earlier in the match," Murray said. "I don't know for what reason, it was extremely lively conditions out there. It was a lot quicker for me, anyway, than what we have been practicing in since we got here. I felt a little bit slow at the beginning.
"And then the positive was that actually towards the end of the match, I made some quite good moves. Like the second to the last point of the match, I moved pretty quickly up to the drop volley and stuff and kind of maintained my serving speeds throughout the match, as well.
"So there was some good stuff, but I think I can get better."
WAWRINKA IMPRESSES ON NEW YORK RETURN
Wawrinka, the 2016 champion, made it eight straight wins at the US Open by cruising past Dimitrov 6-3 6-2 7-5.
The Swiss star, who has failed to go beyond the second round at a grand slam this year, capitalised on an error-riddled display by Dimitrov.
Wawrinka mixed 30 winners with 37 unforced errors, while Dimitrov committed 42 unforced errors.
ANDERSON SCRAPES THROUGH
Runner-up in 2017, Anderson was pushed by Ryan Harrison before winning 7-6 (7-4) 5-7 4-6 6-3 6-4 after four hours and 14 minutes.
Anderson served 28 aces and hit 76 winners to get through the marathon encounter.
RAONIC, THIEM PROGRESS AS SHAPOVALOV SHOWS SPORTSMANSHIP
Milos Raonic had few problems against Carlos Berlocq, winning 7-6 (7-4) 6-4 1-6 6-3, while Dominic Thiem cruised past Mirza Basic 6-3 6-1 6-4.
Meanwhile, Denis Shapovalov took centre stage with an amazing show of sportsmanship against fellow Canadian teenager Felix Auger-Aliassime.
Shapovalov consoled and embraced Auger-Aliassime, who retired due to illness when trailing 7-5 5-7 4-1.