World number one Djokovic, who had not played since losing an Australian Open semi-final to Jannik Sinner on January 26, is chasing a sixth title at the desert venue in the season's first Masters event.
The 36-year-old Serb captured the 400th Masters-level victory of his career, joining Rafael Nadal as the only men to reach the 400 milestone at the elite level.
The 24-time Grand Slam champion has won his last 11 Masters matches, collecting titles last season in Cincinnati and Paris Bercy.
Djokovic claimed the opening set in 35 minutes with two service breaks but had to come from a breakdown in the third against his 69th-ranked Australian opponent.
Vukic held to 6-5 in the second set and landed a reflex service return winner on the line to square the match at a set each.
In the third set, top seed Djokovic broke for a 3-2 edge and closed out victory with a second break after just over two hours, notching his 51st win at the tournament where he first competed in 2006.
"It was difficult to go through him. He played amazing," Djokovic said of Vukic. "He was ripping his forehand and crushing his serve.
"In the third set I managed to crack the code. I stepped it up and finished the match in great style."
Danish seventh seed Holger Rune was handed a free ride into the third round when former Wimbledon finalist Milos Raonic of Canada pulled out of their match with an injury.
US 12th seed Taylor Fritz, the 2022 winner, dispatched Alejandro Tabilo of Chile 7-6 (7/2), 6-2 in 73 minutes, pumping out 14 aces among his 27 winners.
"I needed to play well to protect my serve," Fritz said. "I always feel confident coming out here."
No. 13 Grigor Dimitrov, a 2021 semi-finalist, advanced past Alexandre Muller of France 7-5, 6-2.
Britain's Cameron Norrie reached the third round over Italy's Lorenzo Sonego 6-4, 6-4.
Last weekend's Dubai champion, Ugo Humbert, the 14th seed from France, defeated American Patrick Kypson by the same scoreline.
In the women's draw, third seed Coco Gauff rallied from four games down in the final set to defeat France's Clara Burel 2-6, 6-3, 7-6 (7/4).
Former number one Naomi Osaka continued her comeback after motherhood as she reached the third round with a 7-5, 6-3 victory over Liudmila Samsonova.
Fifth-ranked Jessica Pegula was knocked out 6-2, 3-6, 6-3 by Anna Blinkova, who took revenge for a loss to the American at the start of the month in San Diego.
Blinkova, ranked 45th, added a second high-profile name to her victims' list after defeating Elena Rybakina at the Australian Open.
Unseeded Emma Raducanu benefitted as Dayana Yastremska retired four games into their match with an unspecified injury, handing the Briton a 4-0 win and a place in the third round.
