The Rockets were even more surprised that he achieved the feat coming off the bench.
Lin tallied 15 points, a career-high 11 rebounds and 10 assists and James Harden returned from injury to score 28 points to help the Rockets to their third straight victory, 106-92. Dwight Howard added 26 points and Terrence Jones had 17.
"That's hard to do," Harden said of collecting a triple-double as a reserve. "It's just hard to be able to score the basketball, grab rebounds and pass the ball and get your teammates involved off the bench as a point guard. It's tough. But he's talented enough to do it and he did it."
Lin is the first Rocket to have a triple-double off the bench since Cedric Maxwell did it on March 31, 1988, against Indiana. Two years removed from "Linsanity" with the New York Knicks, the undrafted player from Harvard is thriving in a backup role in Houston, averaging 13.4 points and 4.5 assists.
"It's kind of humbling to think about the whole journey and now this," he said. "It's another cool thing."
Harden sat out the last two games with a bruised left thumb. It showed no signs of bothering him Saturday, when he also had four assists and three rebounds. He made 10 of 17 shots after hitting just eight of 24 shots in his previous two games combined.
"I need to injure my hand more often," he joked. "I shot it better than I've been shooting before. I haven't been shooting the last couple of days so I didn't know how it was going to react to it, but I just had confidence in my abilities and just went out there and did it."
Patrick Beverley didn't score, but helped the Rockets everywhere else with 10 rebounds, eight assists and a career-best five steals.
"You have to give credit to their two guards," Cavaliers coach Mike Brown said. "Patrick Beverley and Jeremy Lin played a heck of a game between those guys. Twenty-one rebounds is phenomenal. They just got after it and went after every loose ball and rebounded."
Houston led by as many as 19 points in the first half before Cleveland opened the second half with an 11-0 run to take a 63-61 lead, its first since the opening minutes of the game.
Cleveland's lead was short-lived as the Rockets roared back by scoring the next 11 points to go back on top 72-63 and hold on for the win.
The Rockets used 3-pointers by Lin and Jones to fuel a 7-2 run early in the fourth quarter that made it 93-78. A layup by Howard followed by an alley-oop dunk by Harden with less than a minute to go pushed the lead to 106-90. Lin's 10th assist came on Howard's layup.
Houston was up by six a few minutes after it regained the lead in the third when another run -- this one 8-0 -- stretched the advantage to 82-68. Harden had a one-handed dunk before a two-handed slam by Howard on the next possession ended the run, brought the crowd to its feet and had Brown yelling for a timeout.
The Rockets led 84-73 entering the fourth quarter.
Five straight points by the Cavaliers got them within seven points early in the second quarter. The Rockets answered with a 14-2 spurt to push their lead to 49-30 midway through the quarter. Lin made six consecutive points in that stretch and Omri Casspi added six points in the run.
The Cavaliers missed shots, committed turnovers and fouled on possession after possession as Houston extended its advantage.
Cleveland finally got back on track when Deng scored five quick points, including a 3-pointer, as the start of a 17-6 run that got the Cavaliers within 55-47. Deng had another 3 near the end of that run and Dion Waiters also hit a 3-pointer.
Another 3 by Waiters with just a few seconds left in the quarter cut the lead to six, but Harden knocked down a 3 just before the buzzer to leave Houston up 61-52 at halftime.
Houston G/F Francisco Garcia missed his eighth straight game with a sore left knee. ... Irving has scored at least 20 points in eight of his last nine games.