Tour match, Taunton: Zimbabwe 285-9 (50 overs) beat Somerset 282-7 (50 overs) by there runs
Stuart Carlisle's third hundred of the tour received fitting reward as Zimbabwe squeezed home in a thrilling finish at the County Ground.
Carlisle plays a sweep shot
Carlisle followed up first-class tons against Worcestershire and Middlesex by making 119 off 121 balls as the tourists posted a healthy total.
But their bowling was again found wanting as Peter Bowler and Keith Dutch both made 93 to keep Somerset in the game.
The county side began the final over needing 11 to win but the loss of Ian Blackwell for 30 proved decisive as Somerset fell short of their target.
Zimbabwe went into the game close to full strength with only Doug Hondo missing from their first-choice side - his place taken by teenage seamer Waddington Mwayenga.
But he was not needed at the start as Heath Streak opted to bat after winning the toss.
Simon Francis removed both openers in an excellent new ball spell but Grant Flower (29) helped Carlisle add 50 to steady the innings.
Carlisle's chief ally, however, was Stuart Matsikenyeri, who weighed in with 66 off 62 balls as they put on 134 for the fifth wicket.
The county side made a bad start in reply as Streak trapped Carl Gazzard lbw for two, but he again looked a class above the rest of the attack.
Dutch's scoring rate kept Somerset in the hunt
Spinner Ray Price bowled James Bryant for 27, but Dutch made his intentions clear with some bold strokeplay as he and Bowler tried to revive Somerset's chances.
They took the score to 219 before Bowler departed, stumped off Doug Marillier, but the spinner's four overs cost 31 as Somerset stepped up the pace.
Dutch hit a six and 11 fours in his 82-ball knock, but he was run out with 24 still needed, putting the onus on Blackwell to see their side home.
Michael Burns and Matthew Wood fell cheaply and Blackwell was run out as Zimbabwe kept their nerve to give themselves a lift ahead of the tri-series against England and South Africa.
Somerset: P D Bowler, C M Gazzard (Wkt), J D C Bryant, K P Dutch, I D Blackwell, M J Wood, M Burns (Capt), G M Andrew, P S Jones, W J Durston, S R G Francis.
Zimbabwe: H H Streak (Capt), T Taibu (Wkt), D D Ebrahim,
D A Marillier, G W Flower, A M Blignaut, S V Carlisle, G B Brent,
R W Price, S Matsikenyeri, W Mwayenga.