The Blues were forced to come from behind after Macaulay Gillesphey's header in the eighth minute.
Cesar Azpilicueta equalised before half-time, but the hosts did not find themselves in front until extra-time, when Marcos Alonso appeared to end any fears of an upset.
But Plymouth were given a glorious opportunity to take the European champions to penalties following a mistake from Malang Sarr.
However, right in front of the travelling faithful, a tame effort from Ryan Hardie was easily saved by Kepa to let a full-strength Blues off the hook.
"What a sickener for him," Sam Parkin said on commentary for talkSPORT. "It'll feel worse than missing in the shootout. What a chance.
"He just didn't catch it, telegraphed it to Kepa. Once you do that, it has to be strong and it wasn't.
"Kepa is an expert in those situations and he makes a very comfortable save."
Nevertheless, Plymouth can leave with their heads held high after giving the European champions a run for their money.
Chelsea boss Thomas Tuchel, watching from home after testing positive for COVID-19, will rue yet more wasteful finishing from his star-studded attack.
The Blues needed their two full-backs to bail them out after the likes of Kai Havertz and Timo Werner spurned an untold amount of glorious chances in normal time.
They escape with a victory, but with Tuchel facing a nervous wait to see if he can join his side in Abu Dhabi for the Club World Cup, this was far from ideal preparation.