An unbeaten partnership of 81 by the pair enabled the tourists draw their match against Middlesex.
Taibu's maiden test wicket started a Sri Lankan slide in which they lost six wickets for 133 runs, four of them to the second new ball.
Sri Lanka were 456 for 7 in reply to Zimbabwe's first innings of 199 on day 2 in the first Test.
Rahmat Shah became the first cricketer from Afghanistan to score a century in Test cricket, during the one-off Test against Bangladesh, in Chattogram on Thursday.
Zimbabwe axed their coach Dav Whatmore and captain Hamilton Masakadza just days before the arrival of India for a five-match limited-overs tour.