The Cavs (2-7) had the NBA's last remaining undefeated team on the ropes with a 13-point lead in the third quarter but the Mavs rallied for their eighth straight victory.
The Cavs got a career night by Zydrunas Ilgauskas, who had a career-high 34 points and 14 rebounds. Jumaine Jones, in his first start of the season, had 23 points. Davis came off the bench and had 19.
Michael Finley led the Mavs with 26 and Dirk Nowitzki, who had four points through the first three quarters, finished with 17.
It was the Cavs' fifth straight loss, but Lucas and guard Bimbo Coles were happy about other changes.
"I absolutely loved the way we played tonight," Lucas said.
"We moved the basketball and we had 27 assists and did all the things that a basketball team needs to do."
Coles said the offense was finally in gear.
"All we had to do was be patient and that's what we did," Coles said. "If we make cuts and reads you can get a lot of good shots in our offense and that's what we did. Except we didn't do that during the fourth quarter. We just didn't make shots."
Ilgauskas was making all of the shots during the third, scoring 12 points. On one play, Ilgauskas saved the ball from going out of bounds with a pass to the cutting Tyrone Hill. Hill made the layup for an 11-point lead, but Ilgauskas was not finished. He nailed consecutive free throws and hit a jumper to extend the Cavs' lead.
"We couldn't guard Ilgauskas at all," said Mavs coach Don Nelson.
The Cavs were cruising and led, 71-58, with three minutes left in the period. Steve Nash and Nowitzki, who average 17 and 22 points respectively, combined for 12 in the third.
The Mavs needed someone to step up and they got it in Walt Williams. Williams nailed two 3-pointers during a 12-0 run that brought Dallas within 71-70 heading into the fourth. The Mavs also received help off the bench from Avery Johnson, who finished with 12.
"A.J. and Walt Williams kept our heads above water when we were about to drown," Nelson said.
Davis, Ilgauskas and Jones rallied the Cavs early in the fourth. The Mavs finally got some scoring out of Nowitzki, who scored six straight points for a three-point lead. The Cavs and Mavs battled but Davis broke the ice with a steal and a spectacular slam over Nash for a two-point lead.
"That's one of my best dunks ever," Davis said. "I rank it with my tip slam I got in Philadelphia."
Unfortunately for the Cavs, their shooting went stale. By the time they made their next field goal, the Mavs were leading by three with 10 seconds left. Turnovers and costly fouls were too much to overcome.
"We had some costly turnovers and I had a couple of them down the stretch," Milt Palacio said. "Walt Williams' shots hurt us and those were momentum breakers but the character of this team tonight was encouraging after playing terrible one night and playing well the next night."