His 45th-minute strike secured a 1-0 win at Turf Moor and ended United's three-match losing run.
It was only United's third win of a troubled season that had seen it lose three of its opening five games in the league going into Saturday's match.
Newly-promoted Burnley is still looking for its first league win of the campaign. While United's narrow victory is unlikely to allay concerns among its fans, Fernandes' goal at least halted a run of three straight defeats in all competitions.
United had not lost four in a row since Louis van Gaal’s second and last season at the club in 2015. The Dutchman was fired at the end of the campaign, despite winning the FA Cup.
Ten Hag avoided emulating his compatriot and will hope the result can spark a turnaround in his team's form, even if Burnley threatened to add to the Dutch coach's troubles.
Fernandes had given notice of what was to come when forcing Trafford into an early save with a shot from an angle, but the home team twice came close to scoring afterwards.
On both occasions it was Zeki Amdouni who threatened. First he saw a header pushed away by the diving Andre Onana and he came even closer to finding the back of the net when sliding a shot past the United keeper, which hit the post.
Evans, starting his first match for United since March 2015 after returning to the club in the summer, thought he'd fired the visitors in front with a header. But his goal was ruled out after a VAR review adjudged Rasmus Hojlund to be interfering with play from an offside position.
Despite being denied on that occasion, Evans played a pivotal role as United eventually took the lead before halftime. With the ball at his feet just over the halfway line, the 35-year-old defender launched a diagonal pass into the box, which Fernandes converted.
Substitute Sander Berge headed over the bar in the last 10 minutes as Burnley went in search of an equalizer.
James Robson is at https://twitter.com/jamesalanrobson
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James Robson, The Associated Press