England captain Alastair Cook urged his side to show the same "relentless" approach that characterised their 266-run win over India in the third Test at Southampton when the series continues at Old Trafford next week.
Thursday's victory at the Ageas Bowl saw England level the five-match contest at 1-1 and, even more importantly, ended a run of 10 successive Tests without a win.
India set a mammoth 445 for victory, collapsed to 178 all out before lunch on the final day, losing their last six wickets inside 25 overs.
England off-spinner Moeen Ali, primarily a batsman, took a Test-best six for 67, including four for 17 in 22 balls Thursday, while James Anderson was named man-of-the-match for a total return across both innings of seven for 77.
Prior to this match, at least seven former England captains had called on Cook to resign as skipper, mainly in a bid to help him get back to his best form with the bat.
However, the left-handed opener ignored their suggestions and was back in the runs at Southampton with innings of 95 and 70 not out, while Ian Bell returned to form with 167 and Gary Ballance made a Test-best 156 in England's commanding first innings 569 for seven declared.
This victory represented England's first win in a Test for nearly a year since they beat Australia at Durham to take an unbeatable 3-0 lead in the 2013 Ashes.
However, the one cloud on the horizon was that Anderson might miss the fourth Test at his Lancashire home ground should an International Cricket Council disciplinary hearing on Friday find against him for allegedly "pushing and abusing" India's Ravindra Jadeja during the drawn first Test at Trent Bridge.
Cook, who oversaw England's 5-0 Ashes thrashing in Australia, was certainly in no mood to get carried away.
"It's a very small step," he said. "It's only one win."
England's dominant display was all the more impressive considering the way in which they had capitulated to a 95-run defeat in the second Test at Lord's.
"We had as good a game as you can have — that's what the turnaround is," Cook said. "We got greedy in the first innings. When you do that, you start getting ahead of the game and can dictate it — and that's what we did."
Now the challenge is to do it all again in Manchester.
"We were relentless, we never let India off the hook at any stage," said Cook. "It takes a lot of skill and determination to do that.
"Now everyone knows what it's like, the challenge is 'can we repeat that at Old Trafford, and try to win the series?"'
