The Clippers lost the first three quarters, including the first 34-16, and faced a 21-point deficit going into the fourth at Fedex Forum.
However, they turned things around to take the lead in the closing stages of the contest - and held on in a tense finale to stun the majority of the support.
Nick Young led the visitors' scorers with 19 points, a total matched by the Grizzlies' Rudy Gay.
The foundations of the Atlanta Hawks' 83-74 Eastern Conference defeat of the Boston Celtics were based on a strong first quarter show.
The Hawks won the first 31-18 and held on to win a game which saw Celtics star Rajon Rondo ejected in the final minute for bumping an official.
Kobe Bryant poured in 31 points for the Los Angeles Lakers as they defeated the Denver Nuggets 103-88 in the first game of their Western Conference play-off series.
A 27-14 first quarter set up the success at Staples Center, where the Lakers' Andrew Bynum equalled an NBA play-off record for blocked shots.
Tony Parker's 28 points helped the San Antonio Spurs defeat the Utah Jazz 106-91 in the first game of their Western Conference play-off at the AT&T Center.