The impressive 18-year-old struck early in both halves to secure his first Premier League goals and send the McDiarmid Park outfit level with Inverness in fifth.
Accies knew they could have leapfrogged Hibernian off the bottom of the table with a victory but were up against it as soon as May fired in the opener after only three minutes.
And the youngster's brilliant second, less than two minutes after the break, ensured the points would stay in Perth.
St Johnstone manager Derek McInnes handed an immediate debut to winger Arvydas Novikovas, signed on loan from Hearts just hours before Monday's transfer deadline.
Hamilton were forced into an unscheduled change just before kick-off when David Elebert picked up an injury in the warm-up and was replaced at right-back by youngster Ziggy Gordon.
The defender's introduction made it a hat-trick of debutants for Accies, with recent signings Mark Carrington, released by MK Dons, and Republic of Ireland Under-23 international James Chambers also making their first starts.
Gordon was put under instant pressure by St Johnstone, as May combined down the Saints left with Novikovas.
However, the Lithuanian took too long as he burst into the box and was snuffed out just as he looked to get a shot away.
But only seconds later, the home side took a fourth-minute lead.
Chris Millar's ball down the right flank allowed Collin Samuel to beat the covering Andy Graham with his pace and the Trinidad and Tobago international's cut-back from the bye-line was perfect for May to drill in from eight yards out.
With Michael Duberry and Steven Anderson repelling everything that Hamilton could throw forward for strike pairing of Mickael Antoine-Curier and Damian Casalinuovo, St Johnstone looked comfortable with their lead.
Accies did at least register a shot on target in the 30th minute but Antoine-Curier's left-foot effort from the edge of the box trundled safely towards home keeper Peter Enckelman.
The Saints goalie looked less comfortable 10 minutes from the interval, however, as Hamilton threatened from a couple of right-wing corners.
With Enckelman flapping at Dougie Imrie's first delivery, Liam Craig was forced to nod off the line as Martin Canning's looping header looked set to sneak in at the post.
Imrie's second corner caused more problems but Canning arrived just too late at the edge of the six-yard box to capitalise.
May almost grabbed a second at the other end on the stroke of half-time after superb combination play with Samuel.
Dave Mackay's low ball to the edge of the area was dummied by Samuel but May found Cerny's legs with his effort on the stretch.
St Johnstone made a half-time switch, with Novikovas making way for Alan Maybury, and the replacement full-back was involved as the home side doubled their lead only a minute after the interval.
May had already raced clear before being denied by Cerny's save but there was to be no stopping his second of the night moments later.
Maybury's shot from the left side of the area was deflected into the path of the teenage marksman and he showed great skill to knock the spinning ball over Cerny with a deft flick of his right foot.
Hamilton boss Billy Reid made a triple change in the 57th minute - replacing Casalinuovo, Carrington and Chambers with Aaron Wildig, Jon Routledge and debutant Tom Elliott - in a bid to find a way back into the match.
The alterations briefly gave the Lanarkshire outfit impetus but they still struggled to create anything meaningful in the crucial last third of the pitch.
Midway through the half, they worked an opening when the towering Elliott knocked on Routledge's free-kick but Steven Anderson brilliantly blocked Antoine-Curier's shot on the turn.
Immediately at the other end, Samuel had a shot hacked off the line by David Buchanan after Duberry had nodded down Millar's corner.
As play continued, May was denied his hat-trick when he struck his volley just too close to Cerny.
Anderson produced another crucial block in the 75th minute to prevent Elliott from getting on the end of Antoine-Curier's cross on the break.
But the visitors looked a beaten bunch as St Johnstone finished the match bossing possession.
Mackay spiralled a free-kick over the bar from a promising position with five minutes remaining but it was to be May's double that separated the teams come the full-time whistle.