Sarwan's 143-ball knock, his highest score in one-day internationals, drove the hosts past Zimbabwe's 273 with an over to spare in St George's, Grenada.
Having enjoyed an easy win in the first match on Friday, West Indies were pushed harder by the tourists, who set a challenging total courtesy of batsman Craig Ervine's 80 runs and Hamilton Masakadza's 60.
West Indies skipper Dwayne Bravo took 6-43 with a lively 10 overs of medium-fast bowling, before Sarwan and Kieran Powell put the home side off to a flying start with 111 for the first wicket.
Powell was out edging Masakadza to wicketkeeper Brendan Taylor in the 26th over and Darren Bravo lasted just two balls, but Narsingh Deonarine steadied the ship with 42 before he was run out.
With 55 runs needed off the final 40 balls, big-hitting Kieron Pollard blasted four fours and two sixes in a breathless knock of 41 from 20 balls to reel in the total and make a dead rubber of Tuesday's final match.
The two teams will play a pair of Twenty20 fixtures in Antigua before tests in Barbados and Dominica.