The Serbian professional struggled to take a strong hold on the opening set in Paris, while Querrey managed to take control of the clay court and execute a number of precise forehand shots and returns to take a one-set lead.
Tipsarevic began to find his form in the second set and prevented his American opponent from dominating the court.
While Querrey tried to force through a two-set advantage, it was the Serbian pro who clinched the set equaliser following an impressive period on Court 1.
Both competitors upped their game for the crucial third set, which turned into a tense affair as both players tried to find a vital break of serve.
The contest continued going by the way of serve, which led to a tie-break that Tipsarevic managed to edge over the 24-year-old, who faced an uphill struggle to win the match.
While Tipsarevic was buoyed by his two-set-to-one lead, Querrey refused to give up on the second-round spot. However, it wasn't enough to trouble the number eight seed, who secured progression through to the next stage of the tournament.