The Jags were on top in an improved second-half display as two terrific saves from on-loan St Johnstone keeper Josh Rae kept them out.
Barry Robson's Raith hurdled Morton but remain seven points adrift of fourth.
Robson said: “My frustration is that the pitch was unplayable. We worked on things all week but we couldn't play out from the back because it was bouncing.
“It was a game of mistakes. We couldn't trust where the ball was going to go.
“I felt we were comfortable. We just lacked that punch at the top of the pitch.”
Thistle failed to create a clear-cut chance in the first period, interim gaffer Graham's hook shot into the side-netting as good as it got.
As well as stifling their hosts, Rovers had two big opportunities of their own.
The first came in three minutes. Jamie Gullan's free-kick was head-flicked on target by Callum Fordyce. Lewis Budinauckas did well to push firmly away at the back post on the bounce.
From another Gullan set-piece, a 19th-minute corner, Finlay Pollock's header flashed just over.
As the home side's first-half frustrations increased, Stuart Bannigan was fortunate to stay on the pitch for a shocker of a challenge. The midfielder's over-the-top foul caught Jordan Doherty on the knee.
The Raith man was fuming as ref Calum Scott settled for a yellow card.
Robson believed Bannigan should have seen red. He added: “You've got to get that right. That's blatant. I...