Kieswetter hit his third boundary through cover for England to reach 128-0 in 15.2 overs and record only the sixth 10-wicket win in Twenty20 internationals — and England's first.
Earlier, Bopara returned figures of 4-10 to restrict the visitors to 125 all out, with only three West Indians reaching double figures.
The tourists collapsed after Samit Patel removed Dwayne Smith (33), who had been the early aggressor, hitting two fours and two sixes to help the West Indies to 51-1.
It was an uncomfortable start to what turned out to be a dream debut as England captain for Graeme Swann, standing in for the injured Stuart Broad.
"I was thinking 'what's the world record for a Twenty20 score?'" Swann joked afterward. "It's natural to fear the worst but the guys didn't panic, they've been brought up on Twenty20 cricket." With five overs remaining, the tourists were 103-3 and looking for another 50 runs, but Bopara piled the pressure on with two wickets in as many balls, bowling Nkruma Bonner off his pads for three and seeing off Christopher Barnwell for a golden duck.
Kieswetter took plenty of credit for that wicket, holding a fine one-handed catch behind the stumps.
Bopara continued to undermine the West Indies innings, first combining with Ben Stokes to run out Andre Russell and then adding his third wicket.
Danza Hyatt was the victim this time, cleaned up with a hint of swing as his side slumped to 112-7.
Derwin Christian was next to go, Jade Dernbach spearing a 90 mph delivery through his defenses, before Jos Buttler ran out Devendra Bishoo with a direct hit from point.
West Indies captain Darren Sammy was last man out with two balls of the innings remaining, Bopara claiming a fourth wicket and Jonny Bairstow holding the catch on his Twenty20 debut.
"Ravi has been getting me out in the nets for two years," Swann said of his star bowler. "I've been telling everyone he should bowl more." Hales and Kieswetter's stand of 208 was England's highest in the shortest format of the game.
Hales, who was out for a duck on his debut against India, smashed eight boundaries and a six for his 62. He also beat his more experienced partner to 50, reaching the landmark in 36 balls.
Kieswetter reached his half-century in 41 balls by scooping a delivery from Sammy over his left shoulder.
"When we started batting we were right on course," Sammy said. "But we lost our way from there and we never caught up.
"We had lots of footage of the England guys and we had plans on how we wanted to bowl to them, but we didn't execute them." The teams meet again on Sunday at the same venue to complete a two-match series that was arranged primarily because the England and Wales Cricket Board still has to fulfill existing agreements with broadcasting partners in the wake of a collapsed 2008 deal with Texas tycoon Allen Stanford.
Stanford was arrested after a fraud investigation by the FBI and Securities and Exchange Commission.
