Mendis batted for nearly five hours on the last day at Harare Sports Club as Sri Lanka held firm and finished on 204-3 in its second innings. The match was declared a draw with 14 overs of the day to go.
Zimbabwe set Sri Lanka 361 runs to win. Sri Lanka was content to bat the day out knowing the draw was enough to take the series.
Zimbabwe continued its second innings from the day before but faced just one ball at the start of the final day before declaring on 247-7.
Zimbabwe captain Sean Williams faced that one delivery, the first of the day, hit it for six to go to his half-century, and then declared. Williams was 53 not out and marched off after flicking the ball from Suranga Lakmal over the backward square leg boundary.
But Zimbabwe couldn't finish the job with the ball despite an early breakthrough to get rid of captain Dimuth Karunaratne.
Sri Lanka was 26-1 at that stage when Karunaratne edged an in-swinger from fast bowler Carl Mumba to wicketkeeper Regis Chakabva.
Mendis was the main resistance, facing 233 balls and hitting 13 fours and a six.
Opener Oshada Fernando also contributed with his 47. He fell first ball after lunch but Zimbabwe took only one more wicket after that, Angelo Mathews for 13.
Zimbabwe was seeking its first win in a test at home in seven years. It made 406 all out batting first with a century from Williams and bowled Sri Lanka out for 293 in its first innings to take control of the game.
Sri Lanka won the first test by 10 wickets and secured its first series since winning in South Africa a year ago.
"I do think Zimbabwe have made great strides, they are a very organized cricket team at the moment," Sri Lanka coach Mickey Arthur said.
"I've seen a massive improvement. Make no mistake, I thought we played very well in test one. We were put under pressure in test two. We had to fight hard to get a draw today and that's congratulations to Zimbabwe. They put us under a massive amount of pressure in this test."
Mathews was named man of the series for his maiden double-century in the first match.