After blowout scores in the first three games, game four was a much tighter affair right from the tip-off.
Both teams matched each other point-for-point in the first half, with a 52-all half-time score setting the stage for an engrossing final two quarters.
Devin Booker bounced back from a lacklustre Game 3 performance to lead the charge for Phoenix out of the break, pushing the Suns to a six-point lead heading into the last term.
However, foul trouble forced him from the game for a substantial part of the quarter, leaving Middleton an opportunity to put the Bucks on his shoulders.
He did just that, capping off a 40-point performance with a crucial six-point run down the stretch which put Milwaukee up 107-101.
Giannis Antetokounmpo had another strong offensive effort with 26 points, but his biggest contribution was a game-breaking block on a dunk attempt from Deandre Ayton which would have levelled the scores at 101 with just less than 90 seconds remaining.
Booker led all scorers in a losing effort with 42, while Chris Paul struggled again, managing just 10 points on 5-13 shooting.
The teams return to Phoenix for game five on Sunday.