For a split second, the hosts thought they had made the breakthrough inside the opening 10 minutes when Matthis Abline's composed finish found the back of the net, but his effort was ruled out for offside to Lens' relief.
While both sides generally cancelled each other out in the early stages of the match, the referee was instructed by the VAR officials to review his video monitor to decide if Les Sang et Or should be awarded a penalty for a handball from Sadibou Sane inside the box. This time, though, it was the home supporters who breathed a sigh of relief, as Clement Turpin concluded that the incident didn't warrant a spot-kick being given.
To Monaco's frustration, they then had a second goal ruled out for offside shortly before the half-hour mark after Edan Diop thought his close-range strike had broken the deadlock.
Les Rouge et Blanc were soon rewarded though for their pressure and persistence, as Paris Brunner met Abline's perfect pass before slotting the ball confidently past Robin Risser from close-range to edge Monaco in front and secure his fourth league goal of the season.
Filipe Luis' side should have celebrated a second goal before the interval, but Abline somehow missed the target from only a few yards out after Brunner's initial strike was palmed away by Risser.
The hosts began the second half brightly and had the ball in the net through Abline but, remarkably, the assistant referee's flag was up for offside once again to the hosts' disbelief.
There was no question that Les Rouge et Blanc deserved their lead but, to the shock of the home fans in the stadium, Lens equalised from out of nowhere after 57 minutes when Matthieu Udol's glancing header from Florian Thauvin's corner flew past Lukas Hradecky.
All of a sudden, Les Sang et Or were full of confidence and should have turned the game on its head just moments later, as substitute Thorgan Hazard steered his header over the bar when he should have hit the target.
Just as it looked like both sides were going to have to settle for a point, Jonathan Gradit inadvertently netted an own goal to put Monaco back in front after 84 minutes and the hosts held on to claim three precious points.
Les Rouge et Blanc have now won four of their opening five Ligue 1 games of a season for the third consecutive campaign.
Flashscore Man of the Match: Matthieu Udol (Lens)