Danny Cipriani was the best player on the field early on but failed to complete the match after tweaking his hamstring.
The Englishman set up two tries and scored another in an early blitz but after his injury the Force hit back, taking the lead in the second half before a late penalty from Melbourne winger Mark Gerrard ensured the win for the home side.
James O'Connor and Richard Kingi pulled out just before the match at AAMI Park but that did not faze Melbourne, with Cipriani at the heart of everything for the Rebels in the first 25 minutes.
The home side started full of purpose and after eight minutes fly-half Cipriani, who this week announced he would be returning to England to join Sale in the summer, put Lachlan Mitchell through a hole to score.
Melbourne dominated possession and their ability to recycle the ball quickly pushed the Force back.
In the 15th minute, Cipriani combined with full-back Julian Huxley, who passed to fellow late-inclusion Lloyd Johansson for a try.
Cipriani got his own try in the 23rd minute.
Melbourne stole the ball off the visitors and Cipriani released Gerrard on the right wing. From deep in his own half, the winger sprinted upfield, faked a kick to step past one opponent before passing inside to Cipriani around the halfway line and the 24-year-old broke clear to score.
He converted the try to make it 21-0 but during his run injured his right hamstring, which forced him off four minutes later.
Immediately the Force got back in the game.
Tries to Force captain David Pocock and Winston Stanley were split by a penalty to Huxley to make the score 24-12 at the break.
Five minutes after half-time, Alfie Mafi blasted through Melbourne's defensive line like it did not exist to score under the posts.
David Harvey converted and scored a penalty soon after and although another penalty from Huxley gave the Rebels some respite it did not stop the Force from taking the lead when Cummins powered over the line in the 64th minute.
Harvey slotted his fourth kick from six attempts and the Western Australians led 29-27.
But having hit the front, the Force let the home team back in the game through penalties and with seven minutes to go Gerrard, Melbourne's third goal-kicker for the night, calmly slotted a long penalty to give his side the win.
The Rebels move up to 10th on the Super Rugby table with 10 points, while the Force are last in the competition with six points from five games.