The victory lifts Bracknell off the foot of Thames Valley Division 4b and just nine points away from safety.
And yet again it was Mahmood who was the architect of the success, hitting a glorious 200 not out as Bracknell declared on 271-6 from 44 overs.
Reading's response lasted nearly 53 overs but they were eventually bowled out well short of the target at 183.
In Division One, Wokingham fell further off the pace after losing their clash with second-placed High Wycombe 2nds by seven wickets.
After electing to bat first, Wokingham made
204-8, a total that Wycombe chased down with ease in just 35 overs.
Finchampstead suffered a similar fate against Beaconsfield as they went down by seven wickets.
James Rendell took 5-61 to restrict Finch to 171-9 and Chris Thomas (72*) then led the home side to a comfortable win.
Meanwhile, Eversley kept their Division 2a promotion hopes alive with a nine-wicket victory over British Airways.
After dismissing BA for 160, Scott Dyer (70*) and Simon Mugava (55) ensured Eversley had little trouble in securing the success.
Royal Ascot lost by five wickets to Purley-on-Thames in Division 3a after Amit Rawal struck a fine 125 not out for the Goosecroft Lane side.