Cilic was only cleared to play last week after he has had his nine-month ban for a doping offence reduced to four months by the Court of Arbitration for Sport.
The former top-10 player served 22 aces and hit 42 winners on his way to victory and will take on fourth seed Juan Martin del Potro in the next round.
"I felt like a kid playing for the first time," Cilic told a news conference. "The feeling was amazing just to be back on the court, to be competing and I enjoyed every moment.
"My thoughts were just on how much I am enjoying it and how I am happy to be back on the court."
Cilic was initially banned for nine months in September after the ITF said he had failed a test for the banned stimulant nikethamide.
On Monday he explained that he had tested positive for a metabolite of nikethamide.
"It shows that nikethamide was in the system some time before and it's completely inactive and doesn't have any effect on the body," he said.
"I'm definitely waiting for the CAS decision in writing and waiting what the ITF will say with all these things."
World number one Rafa Nadal said he was happy that Cilic had returned to competitive tennis.
"The only thing that I can say is that I am happy to see Marin back on tour," he told a news conference.
"He's a good guy and a great player. I don't know what happened, but if he's back, it's because it's fair that he's back. That's all. Happy for that."
The Spaniard won the tight opening set by converting the only break point, but was pushed hard thereafter by Tomic before producing a superb final tie-break to win 6-4 6-7(4) 7-6(1).
Lopez's wayward serving - he got less than half his first serves in - often put him on the back foot, but he attacked Tomic's second serve effectively in a tough-fought encounter that saw both men miss repeated break-point chances in the final set.
The world number 29 turned on the style in a near-flawless deciding tie, however, claiming victory and a match against Switzerland's Stanislas Wawrinka in the next round.
Kei Nishikori of Japan beat local hope Julien Benneteau 6-4 6-2. He will face another Frenchman in the second round in world number 10 Jo-Wilfried Tsonga.
Lukas Rosol, who beat world number one Rafael Nadal at Wimbledon earlier this year, cruised past Jeremy Chardy 6-3 6-4 to earn a second-round match against world number four David Ferrer.
Paris Masters: Round 1 results
Pierre-Hugues Herbert (France) beat Benoit Paire (France) 6-2 6-2
Kei Nishikori (Japan) beat Julien Benneteau (France) 6-4 6-2
Fernando Verdasco (Spain) beat Ernests Gulbis (Latvia) 7-6(3) 7-6(5)
Marin Cilic (Croatia) beat Igor Sijsling (Netherlands) 5-7 6-1 6-4
Feliciano Lopez (Spain) beat Bernard Tomic (Australia) 6-4 6-7(4) 7-6(1)
Robin Haase (Netherlands) beat Denis Istomin (Uzbekistan) 7-6(8) 6-3
Santiago Giraldo (Colombia) beat Adrian Mannarino (France) 6-3 2-6 6-4
Lukas Rosol (Czech Republic) beat Jeremy Chardy (France) 6-3 6-4