The British No 1 had lost all four of the sets he had been involved in over the first two days of competition in the Philippines but finally got off the mark on day three.
After losing two straight doubles sets while partnering Maria Sharapova, Murray teamed up with Kirsten Flipkens to defeat Serena Williams and Lleyton Hewitt 6-1??in the mixed doubles.
He then defeated Nick Kyrgios 6-5 in the final singles set of the match as the Mavericks clinched overall victory by five points.
The Mavericks won four of the five sets, with Mark Philippoussis beating fellow Australian Pat Rafter 6-2 in the legends clash and Treat Huey and Jo-Wilfried Tsonga defeating Krygios and Tomas Berdych 6-5??in the men???s doubles.
In the women???s singles, Williams claimed the lone win for the Slammers by seeing off Flipkens 6-3.
The other match on Sunday featured the Indian Aces and UAE Royals, with the former side clinching a 28-20 victory.
The Royals??? Kristina Mladenovic beat Ana Ivanovic of the Aces 6-4 in the opening set, but the other four were won by the side representing India.
The Aces won all three of their matches in the Philippines to go to the top of the four-team table on 12 points, two ahead of the Royals.
The Mavericks??? victory puts them in third with seven points while the Slammers are bottom on four points having lost all three of their matches so far.
After a day off on Monday, the competition resumes on Tuesday with the first of three days of play in Singapore.
Watch the first day of IPTL competition in Singapore live on Sports 3 HD from 8am on Tuesday.