The home side dominated the first half, with top-scorer May and skipper Dave Mackay both hitting the woodwork, but they eventually forged ahead in the 70th minute when midfielder Davidson headed in from close range following a David Wotherspoon corner.
May made sure of the points when he curled the ball in from 20 yards three minutes later, but in the end it turned out to be as comfortable a victory as Tommy Wright's side would have had all season.
Saints skipper Jim Goodwin returned from a two-game ban to take his place in midfield, replacing John McGinn, who is serving a one-game suspension, while Christopher Dilo replaced Marian Kello in the Buddies' goal as manager Danny Lennon named only six substitutes.
There was a minute's silence before the game in tribute to former St Johnstone player Ian Redford, who died on Friday.
An unchanged Saints side controlled the first 45 minutes with some conviction without being able to get the ball in the net.
Numerous attempts on the St Mirren goal began in the seventh minute when midfielder Wotherspoon forced Dilo into a decent save with a long-distance drive, although the corner came to nothing.
Moments later the Buddies' replacement keeper was less convincing when he batted a clearance off the on-rushing May and was glad to see the ball rebound behind for a goal-kick.
The busy St Johnstone striker then hit the top of the bar with a shot from the edge of the area after Hasselbaink and midfielder Murray Davidson combined at the edge of the box.
The Perth side were well on top and in the 24th minute a chance presented itself when May, with a fine reverse pass, sent Hasselbaink clear of St Mirren full-back Jason Naismith.
The former Buddies forward won the race for the ball with Dilo, but toe-poked it inches past the post from the edge of the area.
The Paisley keeper then did well to get his hand to an angled-drive from May, but soon had to rely on the woodwork to save him again.
In the 33rd minute, after Goodwin was penalised for a foul on Davidson 25 yards from goal, Mackay beat Dilo with his curling free-kick only to see the ball crash off the bar, with the Paisley side eventually clearing their lines.
The visitors' first real attempt on goal came a minute before the break when midfielder Paul McGowan fired wide from the edge of the box.
St Mirren started the second half in a more positive mode, forcing the home side back for the first time in the game, but St Johnstone soon reasserted themselves.
Goodwin, booked for a foul on May in the 65th minute, was shown some leniency by referee Calum Murray after a further two fouls, to the annoyance of the home support.
However, those fans soon changed their tune when Davidson forced in a Wotherspoon corner after a weak Dilo punch to give the home side the lead.
And they they were further elated three minutes later when May's curling effort from 20 yards beat Dilo and went in off a post.
St Mirren appeared to have little to say about their predicament as the Perth men piled forward in the search for more goals.
The home side passed up on more chances before keeper Alan Mannus made a good save from St Mirren substitute Stephane Bahoken, on for Adam Campbell, in injury-time to ensure a clean sheet.