Chasing a modest 98 runs for victory, the Indians romped home with five wickets to spare after initial hiccups. The first match of the series had ended in a draw.
Wicket-keeper Karuna Jain (34) and skipper Mithali Raj (22) held the inning together to see the visitors through after opener Rumeli Dhar departed with the score at six.
For England, who were bowled out for 305 in the second innings, spinner Holly Colvin proved to be the only successful bowler with 2-26.
However, it was Jhulan who was the main architect of the Indian victory as she wrecked the England line-up in both innings to become the first Indian to take 10 wickets in a Test match after grabbing five in each innings.
The all-rounder became the 11th Test bowler to acheive the feat.
Earlier, resuming on 205 for two, England lost skipper Charllotte Edwards, who added only five more to her overnight 100 before becoming Jhulan's victim.
Edwards and Caroline Atkins (68) had added 178 for the third wicket and Jhulan made sure that no England player could settle down after that as she claimed the wicket of Jenny Gunn (4).
Beth Morgan and Jane Smit compiled 43 for the seventh wicket as the home side crashed to 305, leaving India 98 to win, which they reached 29.2 overs.
India: First Innings (307 all out, Anjum Chopra 98, Mithali Raj 65, Isa Guha 4/61) Second Innings (98 for 5, Karuna Jain 34, Holly Colvin 2/26)
England: First Innings (99 all out, Charllotte Edwards 26, Jhulan Goswami 5/33) Second Innings (305 all out, Charllotte Edwards 105, Caroline Atkins 68, Jhulan Goswami 5/45)