Normal order appeared to have been restored when the 20-time Grand Slam champion comfortably claimed the first set against Bautista Agut.
The 20-times Grand Slam victor has produced a series of lacklustre performances in Shanghai, his first tournament since suffering a shock fourth-round defeat by John Millman at the U.S. Open last month.
Coric didn't offer Federer a break point opportunity, while managing to break Federer's serve in the opening game of both sets.
Roger Federer said that he did not want to lose in front of his young family as he was pushed all the way for the second match in a row at the Shanghai Masters yesterday.
Switzerland's Roger Federer hits a return against Croatia's Borna Coric during their men's singles semi-finals match at the Shanghai Masters tennis tournament on October 13, 2018.
The Serbian second seed was stunned by the Italian - ranked 72 in the world at the time - in the French Open quarter-finals earlier this year.
Djokovic and Zverev met on clay in the final of the Rome Masters in May last year, the 21-year-old German winning 6-4, 6-3.
"I wasn't - I feel like - playing as well as I'm playing today", he warned, adding, "but also he has improved a lot and he has established himself as a top player". Djokovic, who endured a turbulent last season with injury and off-court issues, said they were "both different players" now.
Djokovic broke to go ahead when the Croatian went long at the end of a rollercoaster sixth game and that was all the second seed needed to close out the opener.
Novak Djokovic cruised through his second-round match, but Juan Martin del Potro had to retire after hurting his right knee in a fall.
"I did everything I meant to do on my end", the 31-year-old Serb, chasing his 32nd Masters title, said. "It's always easier to get there - but then staying there is always the tougher part".