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Zimbabwe had declared overnight on 247 for seven to set Sri Lanka an improbable target of 361 in 98 overs, and at 107 for one in the 39th over, the tourists may have felt in with a chance of victory.
But when that became 140 for three, they gave up the chase and instead batted for the draw, reaching 204 for three at the close.
Mendis was superb for his 116 from 233 balls, a seventh Test century, first as an aggressor in the chase for runs, and then for his stoic defence when it became apparent that a draw was the best result possible for Sri Lanka.
The two matches are not for Test Championship points as Zimbabwe, briefly suspended from international cricket last year for government interference, are not part of the competition.
Zimbabwe made an early breakthrough at the start of the Sri Lanka second innings when Sri Lanka captain Dimuth Karunaratne (12) edged seamer Carl Mumba to wicketkeeper Regis Chakabva.
But Mendis and opener Oshada Fernando (47) put on 81 in 24.3 overs as Sri Lanka sensed there were still runs in the pitch, before the latter was trapped leg before wicket by off-spinner Sikandar Raza, who finished with career-best match figures of 8-176.
When the dangerous Angelo Mathews (13) was caught at mid-on by Craig Ervine off seamer Victor Nyauchi, the tables turned in the favour of the hosts.
That was a sign for Sri Lanka to baton down the hatches, and Mendis and Dinesh Chandimal (13 not out) ensured Sri Lanka leave Zimbabwe with the series win.
Brief scores
Zimbabwe 406 and 247-7 (B. Taylor 67, S. Williams 53 not out, P. Masvaure 35, Sikander Raza 34; V. Fernando 2-43, L. Embuldeniya 2-81)
Sri Lanka 293 and 204-3 (K. Mendis 116 not out, O. Fernando 47)
Toss: Zimbabwe
Result: Match drawn
Man of the match: Sikandar Raza
Series: Sri Lanka win the two-Test series 1-0
Man of the series: Angelo Mathews
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