Brecel has struggled for big performances since winning the World Championship in 2023, but the Belgian started in commanding fashion at Alexandra Palace to stretch to a 3-1 lead in a race to six frames.
However, Wakelin hit back with a run of 67 in the fifth frame to close the gap to 3-2.
The pair then traded frams again to make it 4-3 as the match appeared to head for a thrilling climax.
But Brecel hit his straps to make three particularly impressive pots to stretch to a 5-3 before closing the match out with a break of 73 to set up a quarter-final showdown with Kyren Wilson.
"That's what happens when you keep getting out of position," Brecel told the BBC of his flashy pots. "(There are) things to work on but I'm happy with the win."
The 29-year-old cut a pragmatic figure in his post-match interview, saying he's still waiting on the form that he needs in order to win in north London.
"It's coming," he said. "Don't know when, but it's coming."
Asked if he's enjoying his snooker, the Belgian responded: "I'm enjoying it very much. Just need to play a little bit better to have a chance here. But yeah, (it) can only get better now."
Earlier in the day, Wilson had beaten China's Zhang Anda 6-4 to book his spot in the last eight.
Masters quarter-finals
Kyren Wilson v Luca Brecel