Dundee United 'will let dust settle' as St Johnstone hero singled out for special praise
The 29-year-old opened the scoring in the first half and set up the second for Melker Hallberg, with May also making a clearance off his own line.
He then hit the woodwork in the second half before United scored what proved to be a late consolation through Tony Watt.
Saints have now put together a three-game unbeaten run, with Davidson saying: “I am delighted with three points first and foremost.
“We worked on things all week and I thought tactically we were really good.
“I don’t really like mentioning players and singling players out but I thought Stevie May was outstanding today.
“First of all, I thought his work-rate was tremendous. He scores the goal, creates a goal and clears one off the line.
“He could have had another second half and that’s what I want to see from Stevie.
“We know he’s got that in him and we believe in Stevie.
“I think his performance was outstanding and typified the result in the end and how we got there.
“The last few minutes were a bit nervy but I thought we had managed to control it in the second half enough not to give away too many chances.
“We could have done better at the start of the second half but then we had chances on the counter to make my life easier.
“But, ultimately, I’m delighted.”
The result leaves the Tangerines rooted to the foot of the cinch Premiership table without a league win to their name so far this season.
New head coach Liam Fox admitted he was struggling to take positives from the game.
The 38-year-old said: “Disappointed, really disappointed. It’s always difficult when you come in 2-0 down at half-time.
“The goals we conceded were poor. A few individual errors gave us a mountain to climb.
“The league table probably tells us that’s why we’re sitting there, individual errors.
“The first goal especially is one ball over the top. We’ve plenty to work on and improve on quickly. That’s the plan.”
Fox added: “We will let the dust settle, we’ll look at the game and be as positive as we can with the players.
“I thought we actually started okay. I would like us to be a bit more ruthless with shots at goal, more crosses in the box, give the fans something to cheer about and hopefully bring them with us.”