New limited-overs coach Giles saw his side end a run of 13 matches without a win in the country in some style, posting a formidable 325 for four and then showing the nerve to withstand a bold chase that eventually subsided to 316 for nine.
England's batsmen set up victory, with Alastair Cook (75) and Ian Bell (85) putting on 158 - England's highest opening stand in India - but the bowlers showed plenty of heart to see off opponents who at times looked capable of reeling in the target with time to spare.
James Tredwell was the pick of the attack with career-best figures of four for 44, while Jade Dernbach struck twice in the 45th over to stem a Mahendra Singh Dhoni-inspired fightback.
The positives for England extended to a solid 44 from Kevin Pietersen, making his first ODI appearance since returning to the format, and a crucial cameo from Samit Patel worth 44 not out in just 20 balls.
There was also a debut for Yorkshire's Joe Root and although he did not bat, he bowled nine tidy overs.