Djokovic needs just 65 minutes to beat Fritz 6-4 6-2 on Court Manolo Santana and book his place in the third round.
The 31-year-old, a two-time champion in Madrid, beat Fritz in Monte Carlo last month before losing in the quarter-finals.
And Djokovic produced a convincing display, dropping just two points on serve in the second set.
After the match, the world No 1 was asked for his assessment and revealed the match was ultimately decided in the first set.
“I thought it was a solid match,” Djokovic told the ATP.
“At 3-3 in the first set, when I broke, that was the turning point.
“And probably the next game, saving break point after a long rally where I was defending, I was lucky he missed a shot.
“I think after that I started to swing through the ball a little bit more. I think Taylor wasn’t at his best, obviously struggling physically or health wise.
“But in general it is a good lead in, a good opening match for me and hopefully it can only get better from here.”
And despite the swift nature of his win, Djokovic said he didn’t mind the quick finish.
He added: “I don’t mind having a quick straight sets win.
“I’ve played a lot of practise sets, I came here five days ago and spent a lot of time hitting on Centre Court.
“So I’m used to conditions and I’m fine with this.”