The hosts were quickest off the starting blocks and almost took an early lead when Dimitri Lienard gained possession in the box and tested Danijel Subasic with a low strike that the keeper struggled to hold.
The opening stages played out at a blistering pace, and the deadlock was broken within five minutes as Jovetic's header from Djibril Sidibe's cross got away from Alexandre Oukidja and nestled into the bottom corner.
End-to-end action continued uninterrupted and Strasbourg were level in the 19th minute when Bahoken won the ball in the area and shot straight into the bottom corner to make it one apiece.
The parity lasted just two minutes as Monaco went back on the attack straight from the restart, eventually working the ball into the path of Lopes into the opposition's box, who curled one into the bottom corner.
Strasbourg's best chance to draw level went begging in the 33rd minute when Bahoken's cross picked out Jeremy Blayac's run into the penalty area, only for his teammate to blaze the ball over the bar unchallenged.
Martin Terrier tried his luck in the 38th minute, latching on to Blayac's headed pass and shooting just wide of Subasic's upright.
Jardim's men gave their hosts a mountain to climb minutes before half time when Keita Balde's cross was rifled home by Fabinho to give Monaco a healthy lead ahead of the interval.
Both sides showed attacking intent in the second period, and Monaco almost extended their advantage in the 57th minute as Jovetic's header from Thomas Lemar's free kick came back off the post.
Blayac was the home side's most dangerous player throughout and he almost reduced the deficit in the 64th minute when he headed Bahoken cross towards goal, forcing Subasic into another save.
Lopes missed an opportunity to kill the game off into the 68th minute, latching on to Jovetic's through-ball to go one on one with Oukidja, only to lose his bottle and miss the target completely.
Monaco defended tightly in the closing stages and absorbed everything their opponents threw at them, but a last-ditch header from Strasbourg's Bakary Kone almost netted them a consolation deep in stoppage time, the defender's header drifting narrowly off target.
The win leaves Monaco seven points ahead of Marseille in the race for the Ligue 1 runners-up spot, while Strasbourg are just three points above the dropzone in 15th.
STRASBOURG (4-3-3): Oukidja, Martinez, Kone, Seka, Lala, Aholou, Lienard, Martin (Grimm 65'), Blayac, Terrier (Corgnet 45'), Corgnet, Bahoken
MONACO (4-2-3-1): Subasic, Jemerson, Glik, Raggi, Sidibe (Toure 64'), Lemar, Fabinho, Moutinho, Jovetic, Lopes, Balde (Tielemans 79')