Djokovic has won every Grand Slam title except the French Open and has made this year's tournament his priority. The Serb lost last year's rain-interrupted final at Roland Garros to Spaniard Rafael Nadal.
The match on center court was delayed and interrupted by afternoon rain. It had little effect on Djokovic's concentration, though, as he swept aside Pella in 1 hour, 26 minutes.
"It's like deja vu from two days ago, you know, coming in and out and warming up five times, but it is the way it is," Djokovic said. "I'm just glad that I finished the match today."
He had 30 winners, broke Pella's serve six times and did not face a single break point on his serve, clinching victory on his third match point when Pella double-faulted.
No. 16 Philipp Kohlschreiber moved into the men's third round when Yen-hsun Lu withdrew because of a right ankle injury. Victor Hanescu also advanced when Dmitry Tursunov retired with a strained left thigh muscle trailing 6-4, 6-6 (3).
Shortly after play resumed following the second rain delay, No. 26 Grigor Dimitrov swept wild card Lucas Pouille 6-1, 7-6 (4), 6-1.
Earlier this month, Dimitrov stunned Djokovic in the second round of the Madrid Open, beating him 7-6 (6), 6-7 (8), 6-3 for the biggest win of his career. He also took a set off Rafael Nadal in quarterfinals of the Monte Carlo Masters last month.
"I think he got more confident as he was getting big wins in last few months, and so he's a tough player now to beat now," Djokovic said. "Even though maybe his style of the game could be better on the hard court or faster surfaces, he's showing that he can play equally well on clay. He pushed Nadal to a tough three sets in Monaco. He beat me in Madrid. "
But Djokovic is confident he can handle Dimitrov in a five-set match.
"It's going to be very physical," he said. "All the hard work that I put into in preparations for this tournament hopefully will play into my advantage and will pay off on the court."
Information from The Associated Press was used in this report.