Spoelstra passed current Heat president Pat Riley to set the record with 455 wins. Miami (15-14) climbed above .500 for the first time in December.
Josh Richardson sank a career-high six 3-points and scored a career-high 28 points to lead the Heat.
Clippers center DeAndre Jordan notched a double-double with 12 points and 20 rebounds. He has four consecutive double-doubles -- his longest streak of the season -- and seven double-doubles in his past eight games.
Both teams shot 38.1 percent in the first quarter, but the Heat jumped out to a 24-17 advantage due to Los Angeles' early woes from 3-point range.
Clippers forward Montrezl Harrell was scoreless in the first quarter but dominant in the second frame, shooting 6-for-7 from the field for 12 points. The Heat held a 46-40 advantage at the break despite being outscored 23-22 by the Clippers in the second quarter. Los Angeles also outscored the Heat 25-23 in the third quarter, shooting 47 percent from the field.
Richardson was 8 of 9 from the field through three quarters, including six consecutive made attempts.
The Clippers (11-17) did not have a lead in the contest until the 6:09 mark in the fourth quarter, when Milos Teodosic made a 3-pointer to earn a 77-75 advantage. Los Angeles got another lead when Lou Williams made a 3-pointer with 1:50 remaining, but the Heat responded, taking an 86-85 edge on Goran Dragic's first points of the second half.
Kelly Olynyk scored nine of his 11 points in the fourth quarter to keep the Heat alive. Dion Waiters had 13 points and six rebounds for Miami. Harrell had 15 points, and Williams and Teodosic each had 13 points for the Clippers.
NOTES: The Heat pushed above .500 for the third time this season, after doing it just once before Dec. 16 last season. ... The Clippers beat the Heat 102-98 on the same date last season in Miami, improving their record to 20-7. ... Heat F James Johnson left the game in the first quarter with a right ankle injury. He did not return. ... Miami F Justise Winslow (left knee sprain) sat out Saturday but will travel with the team Sunday for its two game road trip against the Atlanta Hawks (Monday) and Boston Celtics (Wednesday). ... Heat C Hassan Whiteside (knee) missed his ninth straight game and will not travel with the team. ... Clippers G Danilo Gallinari (left knee) sat out for the third straight game. G Milos Teodosic (rest) returned after having the night off Friday. G Austin Rivers (concussion) was out.