The Swiss maestro and Novak Djokovic strolled into the second round after their opponents retired hurt early in the second set.
Early on in the encounter, there were concerns about Klizan, who was seemingly struggling with a leg issue, with the Slovak hobbling about on court.
On Tuesday, Roger Federer's first-round match is the third scheduled match on Centre Court. Klizan had called for the trainer at the change of ends after the end of the first set but he couldn't prolong things for much long. "It is the cradle of tennis history and it is a special feeling to walk onto this court".
"This year I made a huge jump mainly through Challengers and after half a year I am more or less at break even". You could see that he wasn't moving once the ball was a couple of feet away from him.
"I don't want to be at the mercy of my opponent. I wish him all the best", he added.
Federer, who hit his 10,000th career ace in the eighth game of the first set, will face either Dusan Lajovic for a place in the last 32.
But the top seed showed glimpses of her best form as she saw off American qualifier Irina Falconi 6-4, 6-4 in 87 minutes on Centre Court.
The Canadian had never played Jan-Lennard Struff before but was given a stiff test by the German before edging through 7-6 (7/5) 6-2 7-6 (7/4).
For the record that unlucky lucky loser was Klizan's compatriot, Lukas Lacko, ranked 105 in the world, a battler who could have done with the £35,000 cheque for appearing - as well as the thrill of playing a three-time Wimbledon champion on the biggest stage in his sport. I just have to pay a little bit more attention, be more aware of it, have more discipline.
He has at least tasted some rare recent success, having broken with tradition to play a pre-Wimbledon warm-up at Eastbourne, where he won his first title since January by beating Gael Monfils last week. On the ATP level we have a different sort of situation, whereas if you can't play, you still get your prize money twice in the year. The 18-time Grand Slam champion will be looking to build on his seven Wimbledon victories, in his bid to overtake the likes of Pete Sampras of the United States of America and William Renshaw of Great Britain, to become the sole leader in terms of the number of Wimbledon men's singles titles won.