Vikram Solanki scored 100 as England reached their victory target of 239 with 41 balls to spare and they now have a chance of wrapping up a 4-0 clean sweep when the final match takes place on Sunday at the same venue.
Solanki's century came off just 91 balls and the total of 238-7 made by Zimbabwe earlier in the day was simply not enough on a good batting wicket.
England's Simon Jones had a good debut in One-Day Internationals with a 2-43 haul and Zimbabwe's Stuart Matsikenyeri made his best ever score for his country of 73 and took two wickets.
Jones had been called in to replace Darren Gough but the new ball was shared by Alex Wharf and James Anderson, though he rose to the occasion when he was called into the attack on his One-Day International debut.
Opener Brendan Taylor edged the ball to wicket-keeper Geraint Jones to leave Zimbabwe on 45-1 in the 16th over.
Dion Ebrahim and Matsikenyeri gave the scoring rate a lift but Matsikenyeri eventually fell after hitting his first half-century in One-Day Internationals.
The breakthrough came in the 36th over, ending a 98-run partnership, as Matsikenyeri top-edged a sweep off Michael Vaughan to short fine-leg.Mark Vermeulen and Elton Chigumbura were then dismissed in two messy run-outs before Hamilton Masakadza hit a rapid 21.
Zimbabwe skipper Tatenda Taibu made 24 before Jones claimed his wicket.
Solanki and Ian Bell then gave England the perfect start as they chased 239 but they made the most of their good fortune when Bell was dropped on 17 and Solanki, twice, on 38.
Bell was out for 53 when he clipped Matsikeyeri to Taibu but by that time the damage was done.
Solanki hit Utseya for a six and then edged towards his century as he built a careful partnership of 53 in 14 overs with Vaughan.
The Worcestershire man, having made 100, was then out holing out to long-off leaving Vaughan (54 no) and Andrew Strauss to steer England home.