On a day when both teams performed below average with the bat, the home side lost their last six wickets for 26 runs after skipper Dwayne Bravo's controversial dismissal to be dismissed for 159 off 44.2 overs on Sunday. (Agencies)
England, their confidence at a low ebb on the back of six defeats in their last seven ODIs, seemed to have frittered away an excellent position in being reduced to 105 for seven in the 32nd over.
However Broad joined Bopara in defying the primary threat of spinner Sunil Narine and survived a few alarms before striking the winning boundary with five overs to spare.
West Indies thought they had removed Broad immediately upon his arrival at the crease to a catch at the wicket off Ravi Rampaul but umpire Rod Tucker's on-field decision was reversed on television review.
He was then put down on three by Bravo diving to his left at slip off the same bowler.
It proved to be the critical miss with Broad finishing unbeaten on 28 and Bopara on 38 not out setting the stage for the deciding third and final match at the same venue on Wednesday.
West Indies had won Friday's opener by 15 runs at the same Sir Vivian Richards Stadium.
"We made it really hard for ourselves," said Broad.
"But Ravi (Bopara) did what we expected of him at number seven and we were able to keep our minds clear on the target required."
On another dry pitch, spinners again proved to be England's most effective weapon, left-arm orthodox bowler Stephen Parry taking three for 32 on debut and earning the man of the match award.
"This is the greatest day of my life," said Parry. "To make my debut, get man of the match and, most importantly, get the win, it's a dream come true."
The other three slow bowlers used by the tourists -- James Tredwell, Joe Root and Moeen Ali -- shared five wickets among them as only Lendl Simmons (70) prospered in a West Indies top-order that once again lacked the technique and application to succeed in the conditions.
Simmons and Bravo were threatening a repeat of their century partnership in the first ODI two days earlier, having put on 52 for the fifth wicket.
But the West Indies captain was ruled stumped off Tredwell by television umpire Marais Erasmus despite lengthy deliberation and the examination of numerous camera angles which appeared to suggest there was enough doubt as to whether wicketkeeper Jos Buttler had effected the dismissal before the ball fell from his grasp.
"They're going to get some harsh words in the dressing room," said a despondent Bravo after the lower-order fell away following his demise, leaving more than five overs unused.
"It could have meant another 30 runs for us."
On a day when both teams performed below average with the bat, the home side lost their last six wickets for 26 runs after skipper Dwayne Bravo's controversial dismissal to be dismissed for 159 off 44.2 overs on Sunday.