Djokovic, who pulled out of the recent Miami Open as he tries to balance his schedule, looked fresh as he broke Safiullin's serve three times in the opening set, and a further two breaks in the second was enough to seal the win.
"I think even the games that I lost I had break points in those games. It is a really great first match at the start of the clay season," he said.
On Sunday, Djokovic overtook Roger Federer as the oldest number one ranked singles player in ATP rankings history, at 36 years and 321 days.
"I met (Rohan) Bopanna yesterday, who is the oldest doubles number one in history. He said we had a combined age of 80, but he does contribute to the 80 more than I do," Djokovic joked.
The Serb, winner in 2013 and 2015, will meet the victor between France's Arthur Fils and Italy's Lorenzo Musetti who play their second round match later on Tuesday. Musetti defeated Djokovic at the third round stage last year.
German fifth seed Alexander Zverev made light work of his second round match, defeating Sebastian Ofner 6-3, 6-4. The Austrian finally managed to break serve when 5-2 down in the second set, but Zverev finished off the job with ease.
Zverev awaits the winner of the match between Tomas Etcheverry and 12th-seeded twice champion Stefanos Tsitsipas.
Hubert Hurkacz is into the second round with a 6-4, 3-6, 7-6 win, but was made to battle by Britain's Jack Draper after the Polish 10th seed looked like dominating early on.
Hurkacz raced into a 3-0 lead in the first set but Draper rallied to level at 4-4, before the Pole broke serve to take the opener. Draper then broke to love twice to win the second set and force the decider.
With Hurkacz serving at 5-4 to win the match, Draper broke serve but it was a relieved Hurkacz who emerged victorious in the tiebreak.
Hurkacz, who also beat Draper at last year's tournament, will face Roberto Bautista-Agut of Spain in the second round.
Alex de Minaur had little trouble seeing off the challenge of former champion Stan Wawrinka, winning 6-3, 6-0 to progress to the second round.
Wawrinka won the title in 2014, but a decade later the Swiss was no match for the Australian 11th seed, who needed only 24 minutes to complete a bagel in the second set, and will face Dutchman Tallon Griekspoor.
American Sebastian Korda also eased into the second round with a 6-1, 6-2 win over Spain's Alejandro Davidovich Fokina, finalist in 2022, but will face a much stiffer test when he takes on world number two Jannik Sinner in the next round.
"Obviously, he's probably the best tennis player in the world right now," Korda said ahead of meeting the Australian Open champion.
"He's had an unbelievable season and it's going to be our first meeting on the clay. I'm just going to try to go out there, try my best, and see what happens."
Carlos Alcaraz, number three seed, has withdrawn from the tournament with an arm injury, and his second round place was taken by lucky loser Lorenzo Sonego who will play Felix Auger-Aliassime.
