Sri Lanka went into the final day needing just three wickets to wrap up the match.
Sri Lanka went into the final day needing just three wickets to wrap up the match, and Herath required less than an hour to claim them as he finished with eight wickets in the second innings, bowling Zimbabwe out for 233.
The left-arm spinner's 8 for 63 were the best figures in an innings by a player in Zimbabwe, while his 13 for 152 were the best figures in a match.
"I am always trying to improve," said the 38-year-old. "I don't think about records and will take each series as it comes."
Zimbabwe's only real hope of pushing Sri Lanka on day five rested with Craig Ervine, who resumed on 65 not out with Zimbabwe on 180 for seven in pursuit of 491 for victory.
But the left-hander was the first batsman to fall as Herath had him well caught by Dhananjaya de Silva at slip for 72.
Carl Mumba was next to go, trapped lbw by the left-arm spinner, and although last man Chris Mpofu provided some entertainment as he lofted two huge sixes, he fell to Herath in the same fashion to bring the game to a close.
"His control was exceptional," Zimbabwe captain Graeme Cremer said of Herath. "He doesn't look like he's doing a lot, but he's got subtle variations that as a batsman you don't pick up.
"Only when you watch the replays afterwards do you realise what he was trying to do."
Opening batsman Dimuth Karunaratne was named man of the series for his 280 runs in four innings.
Zimbabwe lost both games by large margins, but took both Tests into the final day and nearly secured a draw in the first match.
"We're happy they've gone five days, and there were a lot of positives for us," said Cremer.
"But a lot of the mistakes we made at crucial times, like dropping silly catches, changed the games in a huge way. We need to improve on that."
The two teams will play each other in a one-day international on Monday, when a triangular series also involving the West Indies gets underway at the same venue.