The Indians rode on Yuvraj's scintillating 118 to post a competitive 292 for nine and then bundled out England for 238 in 47 overs to take a 2-0 lead in the seven-match series.
The 26-year-old Yuvraj, who recovered from a back injury just in time to be drafted into the team, came out with a stunning all-round display to play the pivotal role in India's victory on a rather slow track at the Maharani Usharaje Trust ground.
Yuvraj, who had blasted an unbeaten 138 off just 78 balls in the first one-dayer in Rajkot to mark his return to form, not only notched up his tenth century but also helped the hosts recover from an early slump which saw them tottering at 29 for three at one stage.
He then proved his ability as a left-arm spinner by returning dream figures of 10-0-28-4 which included the prized scalps of Andrew Flintoff, Kevin Pietersen and Owais Shah.
The Punjab swashbuckler stitched 134 runs for the fourth wicket with the in-form Gautam Gambhir (70) while the lanky Yousuf Pathan provided the late sparks to the innings with an savage unbeaten 50 off just 29 balls.
The England innings never really got the momentum to overhaul India's target with none of the batsmen really getting a big knock to keep them in the hunt. Owais Shah (58), Andrew Flintoff (43), Matt Prior (38) and Kevin Pietersen (33) got the starts but could not hang around long enough.
India's Yuvraj downs England with bat and ball
The two teams will now travel to Kanpur for the third game to be played at the Green Park stadium on Thursday.
England's innings began on a disastrous note with opener Ian Bell being run out in the very first over, thanks to a brilliant piece of fielding by Suresh Raina whose direct hit at the non-striker's end gave India the first wicket.
Matt Prior and Owais Shah then steadied the innings to some extent with a 96-run partnership for the second wicket. The two batsmen were quite content in keeping the scoreboard ticking with pushes and nudges while hitting the occasional boundary.
The introduction of the spinners from the 16th over onwards chocked the runs for the visitors, resulting in the asking rate climbing beyond eight runs per over.
The tourists lost the wickets of Shah (58) and Prior (38) in the span of three overs to tilt the scale in India's favour at the stage.
Yuvraj accounted for both the wickets, first trapping Shah leg before wicket and then bowled Prior with a ball that turned a bit.
England opted to take the batting powerplay from the 32nd over and suddenly the runs started coming briskly with captain Kevin Pietersen and the dangerous Andrew Flintoff belting 59 runs in those five overs.
The third match will be played in Kanpur on Thursday.