Jacks' second ODI half-century helped England to a winning total of 206-4 in the 33rd over in a match which was low-scoring compared with the series-opener in which 651 runs were scored.
England sent the West Indies in at the Sir Vivian Richards Stadium and bowled out the home team for 202 in 40 overs. Shai Hope top-scored with 68 after his match-winning 109 not out in the first match which the West Indies won by four wickets.
The West Indies slumped to 23-4 after seven overs before Hope restored the innings in a 129-run partnership with Sherfane Rutherford, who scored 63.
Hope reached his 25th ODI half-century from 44 balls and scored his 68 runs at a run-a-ball, trying to give impetus to an innings that flagged a little in the middle stages. Rutherford's maiden half-century came from 71 balls.
Jacks gave the England innings a solid foundation. He shared a 50-run partnership with Phil Salt (21) for the fourth wicket and reached his half-century from 43 balls. His was the fourth England wicket to fall with a total of 116 in the 20th over.
While Zac Crawley and Ben Duckett both were out for 3, Henry Brook and Jos Buttler took charge and carried England to victory with 17.1 overs to spare.
Buttler finished 58 not out, Brook 43 not out and the unbroken partnership was worth 90.
At 36, Buttler reached 5,000 career runs in one-day internationals, following West Indies captain Shai Hope who reached the 5,000-run milestone in the first ODI. Hope reached 5,000 runs in 114 innings, Buttler in 153.
Buttler registered his 26th ODI half-century from 43 balls just before the end, reaching the mark with a six off the bowling of Oshane Thomas.
“It was a must-win game today and we put in a brilliant performance,” Buttler said. “I've been searching for some form, and spending some time in the middle was great. There's no substitute for that.
“Being not out at the end to get your side over the line is a great feeling.”
The West Indies began poorly when Alick Athanaze was out in the fourth over, caught by Buttler off a sharp delivery from Gus Livingstone. Curran then returned to form by dismissing Keary Carty (0) and Brandon King (17) to leave the West Indies innings teetering at 23-4. It was Curran's first haul of three wickets or more in nine ODIs since March.
His 0-98 in the first match was the most expensive ODI spell ever by an England fast bowler.
“It was a tough day the other day but you've got to keep trying to move forward and bounce back,” Curran said. “We lost that game the other day but bounced back and we're pleased.”
Hope and Rutherford stayed together until the 30th over when Rutherford was caught by Salt from Livingstone's bowling. Hope fell four overs later, bowled by Livingstone and the rest of the West Indies order offered little resistance.
“We put pressure on ourselves by how we batted,” Hope said. “We didn't play situations smart enough and that's what caused the downfall in the batting.”