Of the 61 first serves he landed in, he won 52, and was broken only three times en route to a 6-3, 3-6, 6-2, 6-2 win over the 2014 US Open finalist.
Another player who needed a decider was Rafa Nadal, as he squeezed past Juan Martin Del Potro to land us a victor from our recommended bet, but the after-effects of these arduous wins for Anderson and Nadal may not help them in their quest to reach Sunday's final. Djokovic has the slight edge at overall Tour-level at 26-25, but Nadal ended a seven-match losing streak against the Serb at Madrid a year ago and also won their only meeting so far in 2018 in the semi-finals of the Rome Masters.
A big-serving match tends to have shorter points than one featuring at least one return-orientated player, and so it proved in these - Anderson and Federer played 67 games in 257 minutes (3.84 minutes per game), while it took Nadal and Del Potro 292 minutes to play 55 games (5.31 minutes per game).
He eventually finished off world number 53 Simon in the match's third tiebreak to move into his second Wimbledon quarter-final where twice champion Nadal is waiting. "I wanted to stay there for all night long", Del Potro said.
'Obviously at the end of this day, analyse things that I've done right, that maybe need some improvement, focus on the next day's practice session, recovery. "If I want to beat him, I have to come to the net very often and play hard with my forehands, with my backhands".
World number one Nadal, the 2008 and 2010 champion at the All England Club, trails Djokovic, the 2011, 2014 and 2015 victor, 26-25 in a rivalry which began at Roland Garros 12 years ago.
Del Potro will have to be firing on all cylinders though - something he was clearly not doing against Simon in cooler conditions on Tuesday as he made a meal of the fourth set.
"I have done a lot of things well since I came back from injury".
He led 40-15 but both match points went begging. "I think I can keep doing damage here".
Add in Nadal, 32, and Djokovic, 31, and it's the first time in the half-century of professional tennis that all four male semifinalists at any Slam are in their 30s.
But just as a record-extending 44th grand slam semi-final appearance beckoned, Federer blinked - and eighth-seeded Anderson seized the moment. "I hope I can get a chance to fight for a trophy". I feel like a lot of aspects of my game can give him a lot of trouble'.
Beyond dispute, Anderson's ultimate performance and recovery on this occasion was the antithesis of a choker, prompting the unequivocal praise from the usually deceptive and masterly Federer himself that "I could not fool him - he seemed to know what shots I was manufacturing and planning - and that was not a good feeling".