Motherwell had gone four matches without a goal but it took less then 40 seconds for Murphy to find the net and he doubled the advantage with a solo effort before half-time.
Nicky Law added a third in the 73rd minute and the game was well and truly over by the time David Robertson netted for the hosts, who suffered their first SPL defeat since August.
McCall was rewarded for an ambitious attacking formation which allowed Murphy to run at Saints from a central position just beside front two Michael Higdon and Henrik Ojamaa, with the Estonian often peeling to the left.
Murphy, normally utilised wide left, scored his only other two goals this season from a similar position when Motherwell won at Kilmarnock in August.
The 23-year-old was quickly presented with the opportunity to break Motherwell's recent duck.
Ojamaa made a positive run down the left and turned inside to shoot. His effort was deflected into the path of Murphy, who steered a first-time left-footed shot out of the reach of Alan Mannus.
Motherwell should have doubled their lead two minutes later when Mannus struggled to deal with Steven Anderson's close passback.
Ojamaa dispossessed the goalkeeper and worked space to shoot but got his body shape wrong and sliced his effort high and wide of the gaping goal.
St Johnstone, with Frazer Wright and Steven MacLean starting again following injury, soon settled and first Liam Craig and then Gregory Tade headed wide from Gary Miller crosses.
Tade's was by far the better chance as he arrived unmarked round the back and met the ball six yards out.
Motherwell, who had Adam Cummins in central defence after Fraser Kerr picked up a calf injury, got back on the front foot and Higdon volleyed just wide from 30 yards before Mannus just managed to steer the ball away from Ojamaa after Chris Humphrey had driven the ball into the six-yard box.
Saints had a spell of pressure but Motherwell survived a series of Craig free-kick deliveries and Murphy doubled Motherwell's advantage with a goal out of nothing in the 38th minute.
Keith Lasley started the move with some good midfield play inside his own half before playing a simple pass to Stevie Hammell, who took the ball forward and helped it on to Murphy on the left wing.
The former Scotland Under-21 international cut inside Gary Miller and ran at the Saints defence, who failed to close him down, and fired a powerful low drive inside the goalkeeper's near post from 20 yards.
Murray Davidson's long-range volley had Darren Randolph scrambling but the ball flew just wide and Motherwell survived comfortably until the break, when Murphy was moved to the left wing for a more orthodox 4-4-2 formation.
Ojamaa had another chance early in the second half when he ran on to Humphrey's through ball into the right channel, but Mannus got out well and blocked the striker's attempt to dink the ball over him.
Rowan Vine replaced Tade on the hour mark as St Johnstone manager Steve Lomas looked to shake up his attack following a flat start to the second half.
Vine soon had a half chance from Nigel Hasselbaink's low cross but he could not get hold of his shot and Randolph saved.
Mannus got down well to hold Ojamaa's long-range drive as Motherwell continued to look comfortable but Saints carved out a good chance in the 70th minute for Craig on the edge of the box, but he blazed over with his right foot.
And Law put the game beyond them three minutes later. The midfielder was taken out by a wild sliding challenge from Davidson but he got up immediately and ran on to Lasley's through ball before lifting the ball over the onrushing Mannus and into the net.
Motherwell could have added further to their lead but Higdon shot straight at Mannus following Humphrey's cutback and Randolph looked like he had ensured the visitors' first clean sheet since the opening day with a stunning diving stop to prevent Hasselbaink headed Vine's cross home from inside the six-yard box.
However, Robertson smashed fellow substitute Vine's cutback high into the net with three minutes left to provide some consolation for the hosts, although Murphy almost got his hat-trick in injury-time when Mannus pushed wide his angled drive.