But the Bucks went on to win 118-115, avoiding a four-game sweep in the best-of-seven Eastern Conference semi-final.
In the Western Conference, the Los Angeles Lakers beat the Houston Rockets 117-109 to level their series at 1-1.
Inspired by the 34 points of Anthony Davis, who combined with LeBron James for 62 points and 21 rebounds, the Lakers held off the Rockets' second-half comeback.
Raptors and Nuggets both win to level series.
Antetokounmpo, who could miss Thursday's fifth game with his side trailing 3-1, had made a strong start with 19 points in 11 minutes of the first quarter before he was taken off.
The 25-year-old, who was named this season's defensive player of the year, had injured his ankle in the third quarter of the third game, but he was declared fit after completing a warm-up on Sunday.
He was averaging 27.6 points and 15.0 rebounds in eight play-off games before Sunday, but the Bucks sealed victory as Khris Middleton stepped up to score 36 points in Antetokounmpo's absence.
"We all fought, especially with Giannis going down the way he did," said Middleton, one of six Bucks players to score double figures in the must-win game.
"He came out and tried to fight for us with a bad ankle. We wanted to have his back and just fight for him, and fight for everybody."