The 7-foot center made 10 of 22 shots, including eight 3-pointers (on 15 attempts) to match the Chicago rookie record set by Chris Duhon in 2004-05. He also grabbed 10 rebounds and made all five free throws.
The Bulls were nursing a 120-119 lead when Markkanen scored his final points moments after New York's Kristaps Porzingis hit a 3-pointer.
Without a timeout, the Knicks were forced to go the length of the court, and Jarrett Jack missed a potential tying 3-pointer with 2.8 seconds remaining.
Chicago beat the Knicks for the third time this season with each margin five points or fewer.
The Bulls never trailed after Kris Dunn hit a one-handed running bank shot through the lane with 58.2 seconds remaining in the second OT that made it 118-116.
After Dunn forced Porzingis to miss a 9-footer with 42.3 seconds left, the teams traded turnovers before Chicago's Justin Holiday hit two free throws with 13.9 seconds to go.
The game reached the second overtime when Porzingis blew past Markkanen in the lane and forged a 112-112 deadlock by making an uncontested dunk moments before time expired.
The contest reached overtime tied at 105 as neither team scored in the final 81 seconds of regulation after Jack's fadeaway. The Bulls missed a chance to win when Dunn was off target on a mid-range jumper with 1.4 seconds left.
Robin Lopez and Denzel Valentine added 20 points apiece for the Bulls, who overcame an eight-point deficit in the third quarter and made 15 of 33 3-point tries. Holiday added 16, David Nwaba contributed 13. Dunn's go-ahead shot capped a 4-of-18 showing that resulted in nine points.
Michael Beasley made his first five shots and led the Knicks with 26 points and 12 rebounds. However, he did not score after regulation and finished 10 of 22 from the floor. Porzingis had 24 points on 11-of-24 shooting as the Knicks shot 50 percent.
Courtney Lee contributed 16 as did Jack, who added 10 assists and 10 rebounds for his second career triple-double.
--Field Level Media
Chicago | New York | |
Lauri Markkanen 33 | Scoring | Michael Beasley 26 |
Kris Dunn 8 | Assists | Jarrett Jack 10 |
Lauri Markkanen 10 | Rebounds | Michael Beasley 12 |
Lauri Markkanen 5 | Free Throws Made | Michael Beasley 5 |
Kris Dunn 5 | Steals | Jarrett Jack 2 |
Robin Lopez 2 | Blocks | Kristaps Porzingis 4 |
Team | Points | FG% | 3PM-3PA | FTM-FTA | Assists | Rebounds | Blocks | Steals | Turnovers |
Chicago | 122 | 45.9 | 15-33 | 17-20 | 21 | 48 | 5 | 10 | 17 |
New York | 119 | 50.0 | 10-22 | 13-21 | 24 | 51 | 9 | 5 | 18 |