The sixth seed struck 20 aces and only dropped one game on serve but was made to work hard at times by the world number 53, who had plenty of firepower of his own and claimed second spot on the fast serve list with a 138 mph zinger.
Raonic has been struggling with a hamstring injury and was beaten in the first round at London's Queen's Club last month, making it the first year he had not won a match on grass before Wimbledon since 2014.
"Just not having that constant back-to-back match play, going through those situations many times over, I think that's where it sort of showed," Raonic told reporters.
"I'm happy with how that got better. I just have to pay a little bit more attention, be more aware of it, have more discipline. It doesn't come as easy."
In a tight first set, the Canadian, beaten by Andy Murray in straight sets in the 2016 final, was a frequent visitor to the net, albeit it with mixed results, and drew on a serve that regularly topped 130 mph to keep him out of trouble.
He stepped on the gas in the second set and looked to be cruising into the second round when be broke Struff in his opening service game of the third set.
But Struff, 27, with only four tour-level wins on the grass in his career, broke back as Raonic was serving for the match, eventually forcing another tiebreak.
The understated Raonic only let his emotions show when he went 6-4 up in the breaker with a backhand winner down the line, pumping his fist and shouting "Go".
He finally broke into a smile when Struff's challenge to a backhand service return that was called wide was overruled by Hawkeye to give Raonic the match.
"Beginning of the first set felt like a deja vu of two weeks ago. I really stepped up and did a better job for the rest of the match," he told reporters.
Raonic, 26, plays Mikhail Youzhny of Russia in round two.
(Reporting by Alison Williams; editing by Ken Ferris)
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