Evans is looking to rebuild his ranking, having dropped from a career-high 21st in the world a couple of years ago to 199th.
Given a wildcard entry at Queen’s, the 35-year-old was handed a tough start against American Tiafoe, who reached the quarter-finals of the French Open this year.
But Tiafoe has often struggled on grass and Evans took full advantage, playing some of his best tennis in years to claim an impressive straight-set win.
Evans dropped more than 110 ranking spots last year when he opted to focus on partnering Andy Murray in the doubles at the Paris Olympics, so it was apt that this impressive display came at the arena newly named after the Scot.
The pair reached the quarter-finals at Roland Garros, with the match the last of Murray’s long and illustrious career.
Asked afterwards about how much Murray has inspired his own career, Evans said: “Not just mine but the whole of British tennis.
“He always has time for everyone and it’s fitting he has an arena called after him.
“The Olympics was one of the best things I’ve done. It is something that will stick with me forever and I am immensely proud to have played with him [Murray].”
Evans started strongly against Tiafoe, fending off a break point before securing the break himself at 3-3.
Tiafoe broke back immediately when Evans overcooked his forehand and momentum appeared to swing the American’s way in a 10-minute spell where his opponent had little answer to him.
But Evans, encouraged by the vocal home crowd, dug in and battled from 5-4 down to secure a second break before closing out the set – helped on his way by coming out on top of a gruelling 37-shot rally.
The momentum was now with Evans and a five-game winning streak put him 2-0 up at the start of the second set.
Evans got a stroke of luck at 3-1 up when his forehand clipped the net cord to drop over and secure a double break.
From then on he closed out the match before receiving a standing ovation from the crowd.
“Days like today, whatever happens this week, is why I’ve been carrying on – to get out here and put my game on the court and enjoy it,” Evans added.
“I’m delighted with the win. It was probably one of my best performances I’ve ever played. I didn’t have to think too much, which has been a bit of a problem lately.”