England were reeling at 83 for 4 before Shah and debutant Wright shared 104 in 14 overs. Shah fired 11 fours and two sixes in an unbeaten maiden ton.
Mascarenhas hit Yuvraj for five sixes in the final over as 114 came in the last 10.
Shah and Wright, drafted in for the injured Andrew Flintoff, steadied rocking England innings with some pulsating strokes, which set up Mascarenhas for a momentus cameo.
The Hampshire all-rounder needed only 15 deliveries to smash his brutal unbeaten 36.
After a dot ball to begin the final over, his first six was actually caught on the mid-wicket boundary by Piyush Chawla, but the teenager then carried the ball over the rope.
There was no doubt about the other strokes, which went progressively further, culminating in a straight drive over a shell-shocked Yuvi's head.
India, trailing 3-2 in the series, seemed to be in the driving seat as England, missing injured all-rounders Andrew Flintoff and Ravi Bopara, tottered on 137 for five after Kevin Pietersen was ludicrously run out for 53.
England's innings started poorly after they won the toss with both openers falling inside the first four overs. Alastair Cook edged the second ball of the day from the dangerous Zaheer Khan and Matt Prior (6) was trapped lbw by Ajit Agarkar.
Ian Bell and Pietersen repaired some of the damage with a 50 partnership before Bell played across the line to young spinner Piyush Chawla and was bowled for a fluent 49 in the 15th over.
Next to fall was England skipper Paul Collingwood in controversial circumstances. Pietersen called Collingwood for a risky single and the skipper was clearly in trouble as MS Dhoni whipped off the bails.
Umpire Peter Hartley was unmoved until a replay of the incident showed that Collingwood was short of his crease. He then called for the third umpire and an angry Collingwood was sent packing after scoring just one run.
A circumspect Pietersen looked set to get after the Indian attack when he too was run out after completing his half century. However, England recovered in stirring fashion with Wright, Shah and Mascarenhas ensuring a competitive target.
England 316 for 6 in 50 overs (Owais Shah 107 n o, Pietersen 53, Luke Wright 50, Ian Bell 49, Mascarenhas 36 n o; Zaheer 1 for 43, Chawla 1 for 44, Agarkar 1 for 63) Vs India