Miami extended their winning streak to three games after dominating Milwaukee almost from the outset to secure a win which saw Erik Spoelstra's side improve to 24-20 in the Eastern Conference standings.
Vincent was one of five Heat players in double figures, with Victor Oladipo and Bam Adebayo catching the eye with 20 points each.
Adebayo hauled in 13 rebounds with two assists while Jimmy Butler added 16 points in his 26min 35sec on court at the Miami-Dade Arena.
Nigeria international Vincent, who re-signed with Miami in 2021 after going undrafted in 2018, credited "perseverance" with his latest impressive showing which followed 28 points in a win over Milwaukee on Thursday.
"Just keep going. It's been a long road, an untraditional route (into the NBA)," Vincent told ABC television in on-court remarks after the win while praising his team-mates.
"My guys are getting me open, and I'm finally knocking down some shots - that always helps," Vincent added.
Miami, who were beaten in the NBA Finals in 2020 and who reached the Eastern Conference finals last year before losing in seven games to Boston, are now within striking distance of the automatic playoff places in seventh place.
Vincent meanwhile says improving defensively will be crucial to Miami's chances in the second half of the season.
"We've got to get back to being a defensive team like we know we can be," Vincent said.
Milwaukee meanwhile struggled to build offensive pressure against Miami in the absence of Antetokounmpo and Khris Middleton.
Two-time MVP Antetokounmpo was ruled out early Saturday with a knee complaint.
Bobby Portis led the Bucks scorers with 15 points while Jrue Holiday was restricted to 12 points.