The Middlesex opener, leading England for the first time in place of the rested Andrew Flintoff, retired hurt with leg cramps in the 31st over before the tourists surpassed India's modest 223 with 44 deliveries to spare.
The five-wicket victory Wednesday was England's first win in the seven-match series following four consecutive defeats. The fifth game in Guwahati was washed out on Sunday.
It ended an eight-match winning streak for the hosts, who rested captain Rahul Dravid, leading all-rounder Irfan Pathan and seamer Ajit Agarkar.
The tourists, who drew the Test series 1-1, wrap up the two-month tour with the final One-dayer in the central town of Indore on Saturday.
England defied stifling 42 deg C (108 deg F) heat at the sun-baked Keenan stadium for a long-awaited success in the otherwise disappointing One-day series.
Strauss, averaging less than 19 in the previous four matches, put on 107 for the first wicket with Ian Bell, who hit 46 in his maiden appearance in the series.
England moved to 198-2 with Kevin Pietersen hitting 33 before three wickets fell for 11 runs to the spinners. But Ian Blackwell sealed the impressive win with a six off Ramesh Powar.
"The heat got to a lot of us, including me," said man of the match Strauss. "But this is India and it was a good experience for us."
Earlier, James Anderson and Sajid Mahmood grabbed three wickets each as England bowled out India with two overs to spare despite a blazing 96 from Mahendra Dhoni on his home ground.
India, electing to take first strike, were reduced to 79-5 before Dhoni combined with Powar (54) to add 107 for the sixth wicket.
Dhoni, the aggressive wicket-keeper, smashed 10 boundaries and three sixes, boosting the Indian total after stand-in captain Virender Sehwag (four) and Mohammad Kaif (15) continued their poor form with the bat.
A tired Dhoni, wrapped in an ice vest to beat the heat, missed his third One-day century by four runs when he lobbed a harmless delivery from Mahmood to Vikram Solanki at short mid-wicket.
Dhoni has been rested for the final One-dayer in Indore where Dinesh Karthick will don the gloves, the selectors announced midway through the Indian innings.
England used eight bowlers to overcome the heat with only left-arm spinner Blackwell bowling his entire quota of 10 overs.
"Most of the credit should go to our seamers," said Strauss. "There was a bit for us in the wicket but we still had to put the ball in the right places.
"They set up the win. We needed a good start to get through and this we were able to get. It feels great to win this one."