Blackman found the top corner from 25 yards in the third minute and St Johnstone never recovered from the blow as they remained bottom of the Scottish Premier League.
Kevin Rutkiewicz put through his own net six minutes before the break and Motherwell were rarely troubled in a professional second-half display.
St Johnstone struggled to retain possession without Jody Morris, who failed to overcome a hamstring injury, and seemed to lose confidence after Blackman's opener.
However, the hosts should have gone ahead in the first minute as they passed up a series of opportunities in front of goal.
Marcus Haber was presented with the chance to shoot from 14 yards but he pulled the ball across the face of goal where Murray Davidson missed his kick and Cleveland Taylor was foiled by a great close-range stop from Darren Randolph.
Danny Grainger quickly sent the ball back into the danger zone but Davidson again failed to make proper contact and Randolph collected.
Saints were made to pay within 90 seconds when Blackman showed them how to finish from a much more difficult opportunity.
Keith Lasley won the ball 25 yards out and teed up the on-loan Blackburn striker, who shot first-time into the top corner with his right foot.
The strike was Blackman's second for Motherwell following his winner at Kilmarnock three weeks ago. St Johnstone struggled to rediscover their early threat with Grainger failing to hit the target with a weak 25-yard free-kick.
Tom Hateley came closer at the other end from similar range as Motherwell comfortably protected their lead.
The home side's main tactic of sending the ball into the box from long range was having little effect and Motherwell carried a threat on the break.
Jamie Murphy's left-wing cross just evaded Blackman, who should have done better in the 25th minute when Chris Humphrey played him through. The striker tried to curl the ball round Graeme Smith but his left-footed strike hit the Saints keeper.
Motherwell went two ahead after Murphy got past Dave Mackay inside the box and drove the ball across goal where Rutkiewicz turned it into his own net.
Alan Maybury replaced Liam Caddis in St Johnstone's central midfield at half-time but the change had little effect as Motherwell's grip on possession became even tighter. Lasley and Steve Jennings controlled the play in central midfield and Murphy and the impressive Humphrey continued to pose problems down the flanks in Motherwell's fluid attacking formation.
Saints could not sustain any passing moves and were reliant on set-pieces to create half-chances for Taylor and Mackay, which only yielded shots over the bar.
Derek McInnes sent on strikers Andy Jackson and Steven Milne in a bid to rescue the contest but there was little improvement.
Milne shot wide from 25 yards after a rare passing move from the hosts and the substitute almost got through the Motherwell defence only for Stephen Craigan to produce an important sliding tackle.
Lasley played John Sutton through at the other end but Grainger came across to block. Motherwell held on easily and Fir Park manager Craig Brown sent Alan Gow on for his debut in injury time.