Milwaukee's superstar Giannis Antetokounmpo scored 32 points and Khris Middleton scored 29 points as the visitors beat Phoenix 123-119 in the fifth final meeting of the teams in the North American basketball league.
Now, Milwaukee is only a victory away from pinching its only second NBA title in history.
It can come at home in match six, which is played the night before Wednesday, Swedish time.
In tonight's match, Phoenix took the lead early and had an advantage of 16 points after the first period.
But Milwaukee bounced back - and passed - after putting up a full 43 points in the second period.
At halftime, it was 64-61 to Milwaukee and after the third period, the away team had extended to a ten-point lead.
But Phoenix caught up in the end and with less than a minute left it was 120-119.
In the closing seconds, however, Milwaukee managed to cement their lead with another three points.
The team thus leads the final series with 3-2 in matches.
Milwaukee won its only NBA title so far in 1971 and played its last final in 1974.