The Clippers won the game 125-118 despite playing without four regular starters on Monday at Staples Center in Los Angeles.
"I take my hat off for our young guys," Morris told reporters. "They stepped up and played their butts off. It was a great all-around win."
The Heat had a 35-33 lead after the first 12 minutes. Los Angeles then outscored Miami 20-9 to open the second quarter. Morris scored 11 points in the frame to help the Clippers earn a 67-62 lead at halftime.
The Heat then outscored the Clippers 29-25 in the third quarter to cut the deficit to 92-91 going into the fourth quarter.
Heat guard Tyler Herro hit a jump shot to give his team a 93-92 lead 26 seconds into the final frame. The Clippers then retook the lead on the next possession and never trailed again.
Los Angeles went on a 7-0 run to take a 100-93 lead three minutes into the fourth quarter. The Clippers led by as many as 12 points down the stretch.
Morris made 11 of 15 shots and six 3-pointers to reach his season-high point total. Ivica Zubac chipped in 22 points and eight rebounds off the Clippers bench.
Clippers guard Lou Williams had 18 points and 10 assists. Terance Mann and Amir Coffee also scored 15 points apiece for Los Angeles.
The Clippers had 31 assists in the victory.
"All of our guys were ready to play," Clippers coach Tyronn Lue told reporters. "It was a total team effort and a total team win. We've had back-to-back 30-assist games. We want to continue to just keep building."
"We had breakdowns in different segments of the game," Heat coach Erik Spoelstra told reporters. "They capitalized on the important [sequences] that swing moments of the game."