Chasing a formidable 329 to win in Antigua, Livingstone's 124 from 85 balls saw the tourists home with 15 balls to spare to complete the second highest ODI run chase ever in the Caribbean.
Phil Salt and Jacob Bethell had hit fifties – the latter his maiden half-century in international cricket - before the stand-in Captain and Sam Curran's resilient fifth-wicket partnership left England needing 100 runs from the last 10 overs.
Livingstone brought up his fifty in 60 balls before accelerating to bring up three figures just 17 balls later.
Earlier, Windies captain Shai Hope had scored 117 from 127 balls to help the hosts rebuild after losing both openers early. Hope was ably supported by Keacy Carty (71) and Sherfane Rutherford (54).
It means the series will be decided in the third and final ODI in Barbados on Wednesday.
The two sides will meeting in ODI action in Birmingham next summer, on Thursday 29 May, and Early Bird tickets are available now if purchased before midnight on 12 December. "I tried to get myself going, then knew we could wait until the end and target their death bowling. Sam Curran played beautifully. He hit his second ball for six and he was off and away. I've played a lot of cricket with him, I know I can trust him at that end."
"We need to be more disciplined. In that first game, we showed when we hit our straps, things happen. We didn't execute well. We gave them a lot of easy options to score and when you play cricket like this, guys will capitalise."