Playing early on Court Philippe-Chatrier on Saturday, the No.1 seed ultimately got past the world No.95 Kovinic in straight sets, though the Montenegrin did not go down without a fight.
Kovinic took all three break points that Swiatek offered up, with two of those coming in the second set, halting what seemed set to be a procession for the favourite.
It has been more than 100 days since Swiatek last lost a match, but the Pole temporarily lost her composure as Kovinic reeled off four straight games to go from 4-1 down to 5-4 up.
The final game of Kovinic's streak was settled by a poor Swiatek backhand into the net as the 20-year-old saw the momentum swing the way of her opponent, who was frustrating the world No.1 with some sublime drop shots.
Swiatek took a moment to recover, donning an extra layer, and responded in the next game by holding to 15, and a stray forehand from Kovinic then handed the 2020 champion a break and the chance to serve out the match.
It was an opportunity Swiatek grasped, and though Kovinic fended off the first match point with a powerful forehand, a return straight into the net confirmed her exit.
Swiatek will face Zheng Qinwen or Alize Cornet in round four.