Britain's Andy Murray (35) got the better of Stan Wawrinka (37) 7-6(3) 5-7 7-5 in a clash of former Grand Slam winners to advance at the ATP Masters event in Cincinnati , the last tune-up before the U.S. Open kicks off in New York from Aug. 29.
Tiafoe had failed to capitalize on five match points against Nick Kyrgios in Washington earlier this month and he struggled to get over the line against Berrettini, squandering three attempts to put the match to bed.
But with the crowd willing him on Tiafoe did not let a fourth chance go by, sealing victory after two hours and 52 minutes.
"People don't understand, obviously results haven't really shown how well I've been playing. I've been playing some great tennis, honestly," Tiafoe said on court.
"I really just needed this. I know it's a first-round match .... But everyone knew why I needed this against a quality player, so it was big. I know I've beaten a lot of these guys, but it hasn't happened of late."
Tiafoe failed to convert any of his eight breakpoint chances against Berrettini, who was at a career-high of sixth in the world rankings in January but has since dropped to 15th.
The only break of serve came in the second set when Berrettini leveled the match. The Italian then saved a match point at 5-6 in the third and two more in the deciding tiebreaker before Tiafoe sealed victory.
Tiafoe will next meet fellow American Sebastian Korda, who defeated Karen Khachanov 6-3 6-4.
In their 22nd meeting, neither Murray nor Wawrinka managed a break of serve in the first set. A double fault from the Swiss in the tiebreak opened the door for Murray, who took the opener when Wawrinka sent a forehand long.
In the second set, a broken racket string led Murray to shank a shot that handed set points to Wawrinka and he converted on his first opportunity to level the match.
Murray and Wawrinka both needed visits from the physios in the third set, which Murray claimed when he ripped a return winner on his fourth match point. He is now 13-9 against fellow three-time Grand Slam champion Wawrinka.
"We're not young anymore and matches like this are a lot tougher than they were when we were in our mid-20s," Murray said.
"Both of us gave our best right until the end."
"I started playing as a kid because I love it," Murray said while fighting back tears.
"And it has taken a lot of effort, a lot of struggles to get back to play at this level again and I want to make the most of it while I'm still able to."
Next up for Murray is fellow Briton and ninth seed Cameron Norrie, who beat Holger Rune 7-6(5) 4-6 6-4.
Croatian Marin Cilic's resurgent season continued with a routine 6-3 6-3 win over Jaume Munar and Argentine Diego Schwartzman found his form late to beat Alex Molcan 5-7 6-4 6-2.
Americans John Isner and Marcos Giron, Finland's Emil Ruusuvuori, Spain's Roberto Bautista Agut and Canadian Denis Shapovalov also advanced to the second round of the Masters 1000 tournament.
