The Bobcats won 96-94 in overtime after trailing by four points with a quarter to play in Cleveland and Al Jefferson was the inspiration for Charlotte, scoring 24 points and claiming 15 rebounds in the visitors' victory.
Kyrie Irving starred for the home side with 44 points but could not get the win for Cleveland.
The victory took Charlotte to a 39-38 win-loss record in the Eastern Conference and ensured they cannot be overhauled by the ninth-placed New York Knicks with less than a fortnight left in the NBA's regular season.
Charlotte ended the first quarter down by four points but blitzed the Cavaliers in the second term to lead 40-33 at half-time.
The home side got on top in the third quarter with 33 points to 22 but were reeled in by the Bobcats in the fourth stanza before Jefferson scored seven of the visitors' 14 points in overtime to clinch victory for Charlotte.
Kemba Walker (20 points) and Cody Zeller (12 and 11 rebounds) were strong performers for the Bobcats, who will compete in the play-offs for just the second time in their 10-year history.
Charlotte sit seventh in the East and moved within a game of the sixth-placed Washington Wizards, who were thumped 96-78 by the fourth-placed Chicago Bulls.
Joakim Noah (21 points, 12 rebounds) and DJ Augustin (25 points) were the main men for the Bulls, who kept the Wizards to less than 20 points in three of the four quarters in Washington.
Chicago moved to a 45-32 record, level with the Toronto Raptors but trailing the Canada-based side on points differential.
Toronto defeated the Milwaukee Bucks 102-98, while the Brooklyn Nets, who sit fifth in the Eastern Conference, trumped the Philadelphia 76ers 105-101.
In other results, the Orlando Magic won 100-92 against the Minnesota Timberwolves and the Detroit Pistons overcame the Boston Celtics 115-111.