After an insipid opening period, May was first to a loose ball for the opening goal before Nielsen's inadvertent slip gifted the second to Nigel Hasselbaink.
Motherwell, who knew they could have gone second with a win, made little impression in the opening exchanges but John Sutton did find some space to meet Simon Ramsden's steepling cross, only to plant his header off-target from eight yards.
Under darkening skies both sides struggled to lift the gloom, Hasselbaink foraging with intent down the left and May booming a shot wide from the angle.
The goal the game craved arrived on 49 as May bagged his eighth of the season, reacting quickest to slot in after Nielsen could only palm away Gary McDonald's overhead kick.
Bob McHugh threatened on more than one occasion as Motherwell were stung into belated action before Shaun Hutchinson headed straight at Alan Mannus from five yards.
But any hopes Motherwell may have had of salvaging the game disappeared as Nielsen slid onto Simon Ramsden's backpass but only succeeded in teeing up Hasselbaink who promptly slotted into the unguarded net (64).
Stuart McCall threw on Zaine Francis-Angol and Craig Moore in a bid to save the day but it was the home side who continued to threaten, Hasselbaink miscontrolling with only the keeper to beat.
Moore did draw a decent stop from Mannus but Nielsen was up to his tricks before the end, another weak clearance giving David Wotherspoon a chance for a third, but he could not profit.