Joris Gnagnon put Rennes ahead on 20 minutes at Roazhon Park before Portugal international Lopes levelled on the half-hour with his seventh goal in his past six appearances.
Monaco extended their unbeaten league run to 16 matches, although the draw means Paris Saint-Germain could wrap up a fifth title in six seasons this weekend if results go their way.
The trip to Rennes gave Monaco an opportunity to swiftly move on from Saturday’s 3-0 defeat by PSG in the League Cup final, but the visitors made a poor start in Brittany.
“It’s not easy to play here three days after the League Cup final, there was a bit of fatigue but Rennes also deserve credit,” Monaco coach Leonardo Jardim said.
“It wasn’t the objective but I think a point is about right for our display. Now we’re only going to have two days to recover. We may have to make other changes to freshen up the team (for Nantes on Saturday).”
Sabri Lamouchi’s men are locked in a five-way battle for a Europa League berth next season and forged ahead when defender Gnagnon turned in Sanjin Prcic’s cross on the half-volley.
Prcic forced a sprawling save from Monaco goalkeeper Danijel Subasic and Gnagnon nearly scored again from the resulting corner as his header fizzed just over the bar.
But Monaco were quick to hit back as Radamel Falcao helped the ball on to Lopes whose low right-footed shot nestled in the far corner with Tomas Koubek unable to keep it out.
Wahbi Khazri wasted a clear chance when he nipped in behind the Monaco defence only for Subasic to alertly spring off his line and produce a crucial block with his legs.
Monaco centre-back Jemerson headed narrowly wide early in the second half but both sides were forced to settle for a point as Rennes made it seven matches without defeat to climb to fifth.
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