Craig slotted home in the 62nd minute to move St Johnstone two points behind their sixth-placed opponents in the Scottish Premier League.
Motherwell skipper Stephen Craigan was disgusted with the decision to penalise him for a penalty-box challenge on Michael Duberry, amid suspicions of handball, and his frustration continued as Saints soaked up some late pressure.
Motherwell had scored six goals without reply in two victories against their hosts this season but St Johnstone have improved markedly since leaving Fir Park bottom of the SPL in November and maintained their unbeaten record in 2011.
They had further cause for optimism with an impressive first start for 18-year-old Stevie May, who caused Motherwell problems with his sharpness and clever running.
Motherwell created the first opening in the 14th minute when Chris Humphrey, St Johnstone's chief tormentor in their previous meetings this term, ran clear down the right wing after sharp passing from Jamie Murphy and Steven Saunders.
The winger kept his composure to send in a dangerous low cross but the ball bobbled as Murphy steadied himself to shoot and Dave Mackay cleared the scuffed shot off the line.
May showed good ingenuity and agility to hook the ball across for Chris Millar but the midfielder got just underneath the cross and his header failed to trouble Darren Randolph.
Neither side could find the extra gear required to break beyond each other's back line before the break, although Murphy almost lit up the encounter when he turned 25 yards out and fired a powerful effort that swerved just wide of the post.
Home boss Derek McInnes quickly silenced a critic in the stand by turning round and shouting back following a complaint when some Saints possession went backwards.
Midfielder Liam Craig soon found half a yard of space inside the Motherwell box just before the break following a lay-off from Collin Samuel, but he was closed down quickly and his first-time effort cleared the bar.
Humphrey was off target after a long run before May produced the most impressive piece of play in the match in the 54th minute. May, who made his debut aged 16, ran from near the halfway line before turning inside Shaun Hutchinson and aiming for the bottom corner, but Randolph got down well to block.
Murray then instantly pointed to the penalty spot when Craigan challenged Duberry for Danny Grainger's corner. The Motherwell captain had turned his back on the ball before jumping as he tracked Duberry's run to the back post but the defender was incensed with the decision and was booked for his protests. Craig kept his composure to send Randolph the wrong way.
Motherwell boss Stuart McCall brought on Esteban Casagolda for Murphy and his side pressed for an equaliser.
Steve Jones burst into life and put in several dangerous crosses but there were no takers, and
Humphrey then came close when he cut in and fired a left-footed effort inches wide.
Casagolda fired over from the edge of the box, Stevie Hammell saw a free-kick deflected over and substitute Jamie Pollock and Saunders were thwarted by some desperate blocks.
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