McCowan came off the bench to net with a shot that deflected in off Mark O'Hara three minutes from full-time at Parkhead.
Brendan Rodgers' side had looked set for a frustrating start to their title defence after Benjamin Nygren, Reo Hatate and Adam Idah struck the woodwork, while Callum McGregor had a goal disallowed following a VAR intervention.
The Hoops were not at their best, but they ended the first weekend of the season two points ahead of Old Firm rivals Rangers, who were held to a 1-1 draw by Motherwell on Saturday.
MORE: Read our round-up of the Premiership's opening weekend here
Former Celtic captain Paul McStay performed the pre-match duties as the league champions' flag was unfurled at Parkhead for the 13th time in 14 years and fourth season in succession.
However, Rodgers' assertion that Celtic need new attacking options was backed up by a performance that lacked inspiration in front of goal.
Rodgers had warned on Friday that he would only consider extending his contract beyond next year if the board met his need for them to show ambition to move the club forward.
He had two close-season signings in his starting line-up in left-back Kieran Tierney and midfielder Nygren.
Rodgers' front three was led by Idah, with Yang Hyun-jun on the right wing and the left flank occupied by Daizen Maeda.
Yang struggled to make any impact before being replaced by James Forrest just before the hour mark, and it was Celtic's midfielders who offered the biggest goal threat.
Celtic's early creativity came from Tierney on his return to competitive action with his boyhood club six years on from leaving for Arsenal.
The Scotland international twice delivered crosses for Idah, who failed to trouble goalkeeper Shamal George, and saw a strike diverted over by Alex Gogic.
Celtic came closest to a first-half breakthrough in the closing seconds when George pushed Nygren's shot on to the bar and saved the Sweden midfielder's headed rebound.
McGregor charged down O'Hara's clearance and fired home midway through the half, but the VAR team disallowed the strike for handball, after the ball appeared to hit the Celtic captain's upper arm.
Idah then volleyed a shot off the post from eight yards after chesting down a Liam Scales cross.
Celtic's pressure was eventually rewarded in the 87th minute when McCowan took Maeda's pass on the edge of the area and smacked a shot that whistled into the bottom corner via the hapless O'Hara's leg.