The underdogs twice took the lead and pushed the Premier League side to the brink of elimination, with Wrexham's Hollywood owners, Ryan Reynolds and Rob McElhenney, watching from the stands as their team threatened another famous upset.
Wrexham struck first in the 18th minute when Sam Smith opened the scoring. Chelsea found a way back just before halftime, however, as Wrexham conceded an own goal that levelled the match heading into the break.
The Championship side regained the advantage in the 78th minute through Callum Doyle, raising hopes of another giant-killing. Wrexham had already eliminated Nottingham Forest on penalties in the third round and were close to claiming a second Premier League scalp.
Chelsea responded late in the match when Josh Acheampong scored to make it 2-2 and force extra time.
In the additional period, Alejandro Garnacho finally found the breakthrough. The winger had missed several earlier chances but made no mistake when he finished from a pass by Dario Essugo to put Chelsea ahead.
Joao Pedro then added another extra-time goal to seal a 4-2 victory and ensure Chelsea's FA Cup campaign continued.
Wrexham nearly forced another twist when Lewis Brunt headed into the net during the second period of extra time, but the goal was ruled out following a VAR review.
The defeat ended a spirited challenge from a club with a rich FA Cup history, including a famous 2-1 comeback victory over Arsenal F.C. in the 1992 third round.
Arsenal survived a determined challenge from Mansfield Town as Eberechi Eze struck the decisive goal in a tense 2-1 victory to send the Gunners into the quarter-finals of the FA Cup on Saturday.
Liam Rosenior has hinted that Chelsea's next generation could get a chance to shine when the Blues face Wrexham in the FA Cup on Saturday, with the head coach naming two academy prospects who travelled with the squad.
Liverpool moved into the FA Cup quarter-finals with a strong second-half performance to beat Wolves 3-1 and keep their hopes of silverware alive this season.
Eddie Howe has insisted Newcastle United will attack the FA Cup with full commitment as they prepare for another demanding clash with Manchester City this weekend.
