Saints had only conceded two goals during that spell, which began with victory at Fir Park in October, but they found themselves two goals down inside 17 minutes at a sleety McDiarmid Park.
Tom Aldred and Danny Johnson both netted from close range and Motherwell ultimately held on for a 2-1 Ladbrokes Premiership triumph with the help of Gillespie’s impressive stop from Matty Kennedy’s first-half spot-kick.
Jason Kerr’s header gave St Johnstone hope with seven minutes left but it was too little, too late for Tommy Wright’s men.
It was Motherwell’s first win in 10 visits to Perth since a Jamie Murphy double helped them to a 3-1 victory in November 2012.
Stephen Robinson’s side were ahead inside two minutes when David Turnbull’s corner made its way beyond the back post where Aldred rushed in to stab home.
The visitors were comfortable in the face of some Saints possession until doubling their lead after Liam Grimshaw got round the outside on the right flank and delivered a low cross towards the near post.
Johnson’s challenge helped set up Turnbull and the striker was on hand to finish from close range after his team-mate scuffed a mis-hit shot straight at him. It was a sixth goal in nine league starts for the former Gateshead man.
Saints were handed a lifeline when Charles Dunne handled after failing to cut out Kennedy’s cross, but Gillespie threw himself to his left to push away the winger’s 26th-minute spot-kick and follow up his save from Celtic’s Leigh Griffiths earlier this month.
Carl McHugh had a header blocked on the line after another Turnbull corner before Saints began to exert some pressure in the final 15 minutes of the half. But Gillespie made fairly routine saves from Kerr, Kennedy and David McMillan.