Mahmood's three for 17 took his tally to nine wickets in this series as some careless batting from the Windies top order saw them lurch to 37 for five inside the powerplay.
Windies captain Rovman Powell and all-rounder Romario Shepherd made sure a total collapse was avoided before Overton snared both batters, plus Gudakesh Motie, to claim three for 20 as the hosts posted 145 for eight after losing another important toss for the third time in a row.
Powell wore a wry grin when Jos Buttler called correctly - all three ODIs and two T20s on this tour have been won by the side winning the toss and batting second - as England looked to move 3-0 ahead in the five-match series.
After the start was delayed by 50 minutes due to a wet outfield, England were in business straight away thanks to Jacob Bethell's direct hit after Shai Hope was sent back by Evin Lewis, who departed in the next over when Mahmood hit a hard length and drew a leading edge to Jofra Archer in the deep.
Archer's 89mph delivery then castled Nicholas Pooran, who missed an airy heave across the line, while Mahmood found a bit of movement to draw a drive off Roston Chase, who edged to slip, while Shimron Hetmyer was bounced out.
Powell launched Archer over deep extra cover for the first of four sixes as he and Shepherd rebuilt the innings. Spinners Rehan Ahmed and Liam Livingstone found themselves on the receiving end of some big hits while Powell got to a 36-ball fifty with a massive six off a Sam Curran half-tracker.