Zakharov totalled 507.65 points during the six rounds. He earlier won a silver medal in synchronized three-metre with partner Evgeny Kuznetsov, and was the silver medallist in the individual event at last year's world championships.
He, who was ninth after his first dive, totalled 500.90 while opening the defence of his Olympic title. The top 18 divers moved on to the semifinal and final on Tuesday.
Troy Dumais of the U.S. was third at 486.60 after rallying from sixth in the fourth round.
Two divers scored all zeros, while two others got low scores for badly botching their dives. Even China made a rare mistake.
Qin Kai, who was leading after four rounds, dropped to 11th when he missed on his toughest dive — a forward 4 1/2 somersaults tuck worth a 3.8 degree of difficulty. He narrowly avoided doing a belly flop and ended up 11th with 451.60.
"At least I got to the semifinals," he said. "Hopefully I will perform better."
Two-time silver medallist Alexandre Despatie of Laval, Que., qualified ninth with 458.55 points. He struggled early, scoring just 70.50 on his first dive, but was solid in his last three dives.
"I was a bit annoyed at the beginning, but it got better as time went on. In the semifinal I am keeping the same dives. I did not make any big mistakes," Despatie said. "I am never the person who arrives in the preliminaries and dives the most impressive dive."
Francois Imbeau-Dulac of St-Lazare, Que., qualified 12th with 449.30 points.
Qin already has a gold medal in London, winning the three-metre synchro with partner Luo Yutong. That was one of the five golds won so far by the Chinese, who are attempting to sweep the eight diving events, just as they nearly did four years ago in Beijing. They won seven of eight, losing the men's 10-metre platform.
Dumais has never finished higher than sixth in three-metre at three previous Olympics. He finally earned his first Olympic medal in springboard synchro with partner Kristian Ipsen.
Stephan Feck of Germany dropped out of the competition after the third round. He lost his grip on his right leg doing a forward 3 1/2 somersault pike and landed on his back, smacking the water as the crowd gasped. He received all zeros from the judges. Feck did his third dive and then withdrew, with officials saying he felt faint.
Jack Laugher of Britain hushed the home crowd when he missed his last dive. He appeared to slip off the edge of the springboard after launching into his jump and earned all zeros. Laugher finished 27th.
Two South Americans also made big mistakes.
Edickson Contreras of Venezuela scored 4.95 for his last dive, a reverse 2 1/2 somersault with 1 1/2 twists pike. He bounced once on the board, turned and walked back. He tried again and landed with his legs smacking the water. Contreras got out, and crouched against the wall with his back toward the pool. He was 28th.
Cesar Castro of Brazil took an extra bounce on his fifth dive and then botched it, earning marks of 3.0 or less. He qualified for the semifinal in 14th.