Hearts entered the field to a warm reception following their Easter Road heroics, which were followed by the resignation of Hibs boss Pat Fenlon - but they were looking for a more positive consequence in the shape of a launchpad for a Scottish Premiership revival.
The home side made a bright start but Hasselbaink headed home in the 28th minute and fellow semi-finalists St Johnstone never looked like relinquishing their lead.
May netted his ninth goal of the season in the 53rd minute when he curled home brilliantly following a spell of intense pressure and, although Hearts kept pressing for a way back, Saints held firm to record a third consecutive victory and clean sheet and consolidate their place in the top six.
The cup triumph had come after Hearts had secured just one point from a possible 21 but they failed to improve on that record and their only positive was that they remain 15 points adrift after St Mirren's match was abandoned amid heavy rain as they led Ross County 2-0.
An early interchange of passes between Jamie Walker, Jason Holt and Kevin McHattie before the former fired just wide from 30 yards suggested the home side's confidence was high and Holt then latched on to Ryan Stevenson's header but shot over from a tight angle.
However, Hearts had a warning when May got past Jordan McGhee and cut back from the byline for Hasselbaink six yards out - but Jamie MacDonald got down brilliantly to block.
Play was scrappy for the next 15 minutes before Saints took the lead. David Wotherspoon robbed Dylan McGowan deep inside the Hearts half and Hasselbaink drove forward and got the ball out to Chris Millar on the right side of the penalty box.
The midfielder's attempted return pass took a deflection and looped into the air and fell for the Dutchman to head down and into the net from eight yards.
The home fans tried to lift their team and Stevenson sent a snap-shot wide before shooting into the wall when Bobby Madden awarded a free-kick after Murray Davidson fouled Holt right on edge of the box.
McGhee slid in but could not turn Walker's driven cross on target but Hasselbaink should have made it two in the 42nd minute when he sent a free header over following Millar's cross.
The pair combined again as Saints broke after a Hearts corner but Millar curled high and wide.
Hearts had a let-off moments after the restart when May was centimetres away from connecting with Wotherspoon's cross on the six-yard line McGhee shot just wide from 35 yards before Saints had another good chance when Wotherspoon's deflected shot fell kindly for Gary McDonald, whose shot lacked power and the Hearts goalkeeper saved.
Saints kept the pressure on and Wotherspoon had two shots blocked in the six-yard box before MacDonald saved brilliantly from McDonald, however the rebound broke to May and he curled into the far corner from 15 yards.
Hearts found it difficult to create chances from open play but they had a number of set-pieces with headers from Callum Paterson, Danny Wilson and McGowan failing to hit the target before McGhee saw one blocked.
However, the St Johnstone defence looked relatively solid and the Tynecastle atmosphere was unusually flat as the final stages played out.