Zimbabwe, who had selected a highly inexperienced squad for the five-match series after 15 capped players made themselves unavailable as part of a selection-process battle with their board, were dismissed in 18 overs after losing the toss.
Sri Lanka, who won the first two one-day internationals in Bulawayo, replied with 40 for one in 9.2 overs.
Zimbabwe's total eclipsed the previous low of 36, Canada's innings score against Sri Lanka at Paarl during last year's World Cup in South Africa.
No Zimbabwe batsman reached double figures at Harare Sports Club, Dion Ebrahim top-scoring with seven. There were four ducks.
Left-arm fast bowler Chaminda Vaas took four for 12 in nine overs for Sri Lanka, becoming the second Sri Lankan to take 300 one-day wickets after off spinner Muttiah Muralitharan.
Vaas obtained swing and movement off the seam and was virtually unplayable on a lively pitch of inconsistent bounce.
Medium pacer Dilhara Fernando shared the new ball with Vaas and also dominated the batsmen on his way to figures of two for 18 in six overs.
Debutant paceman Mohamed Maharoof claimed three for three.
RECKLESS BATTING
Although Zimbabwe were outclassed by quality bowling on a difficult pitch, they contributed to their own downfall with a reckless batting approach. The last nine wickets crashed for just 17 runs.
Zimbabwe's innings began to disintegrate in the eighth over, when Ebrahim drove loosely at a ball from Fernando and was caught behind by wicketkeeper Kumar Sangakkara.
Seven balls later, Zimbabwe had plummeted to 19 for five, losing four wickets for just one run. Among them was captain Tatenda Taibu, who held his team's innings together in the first two matches of the series with top scores of 96 not out and 35.
On Sunday, however, Taibu was dismissed first ball, leg before to an inswinger from Fernando that straightened after pitching and struck him on the back pad.
Taibu was Fernando's second victim in as many balls, but Elton Chigumbura survived the hat-trick ball before being bowled by Vaas for a duck in the ninth over as he aimed an expansive drive.
Zimbabwe's unluckiest batsman was opener Brendan Taylor, caught off the back of his bat by Tillekeratne Dilshan at short leg for four after a short delivery from Vaas had struck him on the shoulder.
