Mumbai scored three excellent field goals, which count as a double strike as per the rules of the tournament, through Gurjant Singh (14th minute), Florian Fuchs (42nd) and Yosuf Affan (59th).
For UP Wizards, who were knocked out of semifinal contention, V R Raghunath (19th penalty corner) and Chinglensana Singh (30th field goal), were the goal-getters.
It was only the fourth win for Mumbai from 10 outings, but it was enough to put them level on points with Kalinga Lancers (25) who play Delhi Waveriders tomorrow in the last round robin encounter.
With both the teams UP Wizards and Mumbai facing a must-win situation for a berth in the last four round, the game got off to a breezy start.
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UP Wizards took the first shy at the rival goal in the second minute but Akashdeep Singh's shot was blocked with his pads by Mumbai custodian David Harte, who had an outstanding game.
Gurjant Singh then hit wide a superb long through ball from his Mumbai teammate Harmanpreet Singh but made amends off a counter-attack later with a field effort, two minutes from the end of the first quarter, that counted as a double strike.
UP Wizards, down 0-2 at the end of the first quarter, attacked with vigour and forced three penalty corners early in the second quarter. They succeeded with the third attempt when Raghunath beat Harte with a shot that hit the board.
Hard-working Mumbai captain Matthew Swann showed a clean pair of heels with his dribbling skills to get past a host of defenders but he was stopped in the nick of time.
At the other end UP Wizards, desperate for the equaliser, got a bonus when Chinglensana hit the roof of the net with a sweep after trapping a goalmouth clearance just inside the circle to ensure UP Wizards trooped off at the end of the second quarter with a 3-2 advantage.
UP Wizards then forced a penalty corner that was wasted and Mumbai counter-punched effectively with a quick move on the left flank that saw Nilakanta Sharma lay an inch-perfect square pass to his right for the opportunistic German Florian Fuchs to shoot home from the top of the circle which completely beat Sreejesh on his left side.
Mumbai pressed on even after going ahead and after missing a few chances got a great goal in the dying minutes after UP Wizards pulled out Sreejesh.
Affan dived full length to connect a centre from Gurjant on his left to complete a memorable day for the home team.