Christophe Pelissier's home side took a shock 31st-minute lead through Serge Gakpe, but Jovetic came off the bench in the second half to equalise.
Monaco Captain Radamel Falcao quickly went in search of his 14th league goal of the season, but twice fired wide before being denied by the legs of Amiens goalkeeper Regis Gurtner.
The Stade de la Licorne burst into life just after the half-hour mark as Togo international Gakpe surged through on goal and confidently slotted into the corner to score his first Amiens goal.
The visitors almost got a leveller on the stroke of half-time, but after Gurtner failed to deal with a high ball into the area, Monaco centre-back Jemerson sent a lob over the crossbar.
Amiens started the second period brightly and almost moved further ahead, but striker Moussa Konate headed over when he was totally unmarked just a few yards from goal.
Falcao went close again as he brought a diving stop from Gurtner with a curling effort from the edge of the box, before Guido Carrillo's header grazed the outside of the post just seconds later.
Having already replaced Rony Lopes with Rachid Ghezzal at the interval, Jardim sent on Jovetic just after the hour mark and it took the Montenegrin international less than six minutes to make his mark.
The former Inter Milan striker grabbed the equaliser by picking out the bottom corner after excellent work from Fabinho to score his second goal for the club.
But it was Amiens who looked more likely to find a late winner as ex-Chelsea forward Gael Kakuta nodded over.
Monaco will now turn their attention to Tuesday's clash with RB Leipzig, when last year's semi-finalists could win and yet still be eliminated from the Champions League.
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