The Bhoys were heading towards a shock result with 45 minutes played after Conor Sammon put the lowly hosts ahead from the penalty spot.
Any hopes that the Jags had of adding to their paltry tally of one point from a possible 63 against Celtic soon faded, however, as Leigh Griffiths bagged a 70th-minute winner after Scott Sinclair had earlier converted from the spot.
Shortly after Olivier Ntcham had almost caught out the opposition keeper with his audacious attempt, Craig Gordon was called into action at the other end to help over Miles Storey's side-footed effort.
Edouard was thwarted by Tomas Cerny with a back-heeled shot just short of the half-hour mark, and that appeared to be a big moment in the game as Mikael Lustig pulled back Storey moments later to concede a penalty.
Sammon made it four goals in three games by sending Gordon the wrong way - the first goal that Celtic have shipped in six games.
Sinclair saw a powerful drive pushed past the post shortly before the half-time interval, and both teams would come close soon after the restart as Ntcham fired wide and Sammon's header was inches wide.
Celtic's leveller arrived 55 minutes in when Sinclair brushed himself down after being felled in the box to find a way past Cerny from 12 yards.
Celtic stepped things up further, with Forrest, Kieran Tierney and substitute Griffiths helping to spark the champions into life with their shots on goal.
The winner soon followed as Griffiths, whose half-time arrival turned the game in the visitors' favour, shrugged off the challenge of Adam Barton and picked out the far corner of the net.
PARTICK THISTLE (4-2-3-1): Cerny; Penrice, Cargill, Keown, Dumbuya; Edwards, Osman; Storey (Erskine 77'), McCarthy, Spittal (Barton 56'); Sammon (Doolan 71')
CELTIC (4-2-3-1): Gordon; Lustig (Griffiths 46'), Boyata, Ajer, Tierney; Brown, Ntcham; McGregor, Forrest, Sinclair (Simunovic 77'); Edouard (Bitton 84')