Dravid fashioned England's dismissal for 237 with astute bowling changes and then hit 65 off 73 balls to help the hosts surpass the modest target with 16 deliveries to spare at the Nehru stadium on Thursday.
England, needing a win to stay afloat in the series, were bowled out in 48.4 overs despite a fine 77 off 82 balls from Kevin Pietersen and 49 from wicket-keeper Geraint Jones.
Some 75,000 home fans braved stifling heat and humidity in this south-western port city to cheer India's eighth one-day win in a row and the 16th in their last 20 matches.
India's 14th consecutive victory while chasing a target surpassed a 21-year-old record set by the West Indies in 1984-85.
Dravid put on 54 for the first wicket with Virender Sehwag (26) and 76 for the second with Irfan Pathan, who contributed 46 off 56 balls.
The Indian captain hit nine boundaries in his 69th one-day half-century before he drove his English counterpart Andrew Flintoff to Matthew Hoggard at mid-off.
There was a minor hiccup when Pathan and Mohammad Kaif were dismissed on the same total of 152, but Yuvraj Singh (48) and Suresh Raina (21) put on a match-winning 72 for the fifth wicket.
Both batsmen fell off successive deliveries from James Anderson with 14 needed for victory, but it came too late for England to salvage a win.
Dravid contained England in the field by using four slow bowlers for 30 overs on a wicket that assisted a bit of turn. The move produced six of the wickets for India.
Pietersen, who missed the previous game in Goa due to a stomach ailment, hit six boundaries and two sixes before Yuvraj claimed two wickets and grabbed two good catches to restrict England.
The tourists had lost both openers, Strauss and Matt Prior, by the sixth over with the total at 27.
Pietersen and Paul Collingwood repaired the early damage by adding 90 for the third wicket before a brilliant return catch by Yuvraj ended the partnership.
Left-arm bowler Yuvraj dived to his left on his follow through to hold a one-handed catch as Collingwood, who made 36, mistimed a drive.
The total had moved to a respectable 153-3 by the 29th over when England lost both Pietersen and Flintoff in the space of eight deliveries.
Pietersen top-edged a sweep off Harbhajan Singh and Yuvraj made no mistake with the skier at mid-wicket.
Flintoff, who made 12, on-drove Yuvraj uppishly to short mid-wicket where Dravid latched on to a low catch.
England soon slumped to 172 for six as Vikram Solanki failed to read Ramesh Powar's off-spin and was bowled for 12.
Sehwag chipped in with the wickets of Ian Blackwell and Gareth Batty in successive overs to reduce England to 203-8.
The remaining three matches will be played in Guwahati (Sunday), Jamshedpur (April 12) and Indore (April 15).