It looked like being a frustrating evening for Celtic until McGregor's late goal sealed a victory that left the Glasgow giants four points behind Premiership leaders Hearts.
Hearts will, however, go seven points clear at the top of the table if they win away to Aberdeen on Sunday.
McGregor's superb effort was Celtic's first on-target effort of the entire game and came beyond the four minutes of added-on time indicated by the match officials.
"We just keep going, keep going, keep going," midfielder McGregor told Sky Sports of a Celtic side still under the caretaker charge of Martin O'Neill following the resignation of former manager Brendan Rodgers.
"St Mirren make it really difficult for you. The boys are working so hard. I'm so glad we got the reward we wanted."
Earlier, Rangers rode their luck to secure a fourth straight league win under new boss Danny Rohl as Mohamed Diomande's effort sealed a 2-1 victory over basement club Livingston.
But the visitors left Ibrox furious after the referee and VAR officials failed to award them a penalty despite replays showing Tete Yengi's shot had struck the arm of Emmanuel Fernandez in the box.
Fernandez powered home a ninth-minute header from James Tavernier's cross to give Rohl's men the lead.
But Livingston, without a win in 10 games, levelled within 10 minutes when Yengi chased a long ball over the top and fired home.
After Yengi's penalty appeal, the striker had a further chance to snatch a winner, only to be denied by goalkeeper Jack Butland when clean through before the Gers had Diomande to thank for snatching the points 12 minutes from time.
Promoted Falkirk continued their fine season with a 3-0 win over Dundee United at Tannadice as home keeper Yevhen Kucherenko endured a miserable match.
Kucherenko spilt a tame shot from Calvin Miller to give the Bairns a third-minute lead, and 19 minutes later, he somehow punched a Falkirk corner into his own net.
Kucherenko's day to forget was complete on the hour mark when he misjudged a high ball forward and was caught hopelessly out of position as Brian Graham beat him to slot home Falkirk's third.
Goals from Kieron Bowie and Jamie McGrath proved enough for Hibernian to beat struggling Dundee 2-0 at Easter Road.
Kilmarnock suffered a sixth straight loss to pile the pressure on manager Stuart Kettlewell as they went down 3-1 at home to Motherwell.
Tawanda Maswanhise struck twice within the first half-hour before a goal from Scott Tiffoney gave Killie hope early in the second half.
But a 68th-minute penalty from substitute Apostolos Stamatelopoulos restored Motherwell's two-goal advantage.