The 2011 champion went down clutching his left shoulder at 3-2 up in the third set but held on to record a 6-4 6-2 6-4 win against the Frenchman.
Djokovic won 77 per cent of his first service points to beat Simon for a seventh consecutive time with all attention turning to how he recovers from what he said was a sore muscle.
Another Frenchman awaits in the last 16, after Jo-Wilfried Tsonga came out on top in his first meeting with world number 147 Jimmy Wang.
Tsonga won through 6-2 6-2 7-5 while Djokovic's final opponent from last year's event, Andy Murray, enjoyed a similarly comfortable time on centre court.
The reigning champion was rarely troubled against Spain's Roberto Bautista Agut as he won all but five of 40 points on his first service to maintain his title defence with a 6-2 6-3 6-2 victory.
A semi-finalist last year, Jerzy Janowicz grinded his way into the third round this time around after a marathon encounter with former world number one Lleyton Hewitt.
Hewitt broke the Open Era record for the most five-set matches at grand slams with 42 as he was beaten 7-5 6-4 6-7 (7-9) 4-6 6-3.
Sixth seed and 2010 runner-up Tomas Berdych was made to wait for his 100th grand slam match win as he was beaten 7-6 (7-5) 6-4 7-6 (8-6) by Marin Cilic.
It will serve as revenge for the Croatian, who lost to the world number six in the final of the World Tennis Tournament in Rotterdam earlier this year.
Grigor Dimitrov, fresh from winning his first grass-court title at Queen's two weeks ago, outlasted Alexandr Dolgopolov 6-7 (3-7) 6-4 2-6 6-4 6-1 while Feliciano Lopez continued his fine record on the surface this year to move past Ante Pavic of Croatia 6-4 7-6 (7-4) 7-5.
The Spaniard has now won 11 of 12 matches on grass, while Argentina's Leonardo Mayer also enjoyed a straight-sets win.
He beat Andrey Kuznetsov 6-4 7-6 (7-1) 6-3 after Kevin Anderson had become the first man into the fourth round of the competition by seeing off Italy's Fabio Fognini 4-6 6-4 2-6 6-2 6-1.
It is the South African's first foray into this stage, at the sixth attempt, after winning 80 per cent of points on his first serve in the pair's first meeting since 2011.
In a rain-delayed encounter against Marcel Granollers, Santiago Giraldo eventually came through their thriller a 4-6 7-6 (7-2) 1-6 6-1 7-5 victor.
The Colombian was 2-1 down in the fifth set when play resumed on Friday but he broke in the 11th game to win through in just over three-and-a-half hours.
Sergiy Stakhovsky was another to bow out - wilting late on in his 6-3 6-7 (4-7) 6-3 6-0 defeat to Jeremy Chardy.