The Premier League giants trailed twice but secured victory to progress to the quarter-finals of the competition.
Here's how the players rated.
ROBERT SANCHEZ: Should have come off his line to clatter Smith for opening goal and just doesn't look confident with the ball at his feet. 6
BENOIT BADIASHILE: Chelsea's game-management at the back was poor as the Premier League defenders should have put this game to bed. 6
TOSIN ADARABIOYO: Made a crucial block to stop Kieffer Moore from scoring at the back post to make it 3-3. 6
MAMADOU SARR: The first Chelsea player to be taken off as boss Liam Rosenior went on the attack. 6
JOSH ACHEAMPONG: Did nothing part from score a superb goal to whack it into the corner to make it 2-2. 6
ANDREY SANTOS: Neat and tidy on the ball but Wrexham got on top of the game in midfield in the second half. 6
ROMEO LAVIA: He hasn't played much of late but is too tippy-tappy in the middle of the park and needed more urgency. 5
JORREL HATO: Was one of Chelsea's best players. He looks class and nutmegging Max Cleworth was his best bit. 7
PEDRO NETO: Sees a lot of the ball but will be disappointed with his end product, including a second half effort that smashed against the bar. 7
RORY DELAP: Created the opening goal for Chelsea but he needs goals to boost his confidence. 7
ALEJANDRO GARNACHO: The more Wrexham fans booed him, the better he got. Played a massive part in first goal and then smashed in the third. 8
SUBSTITUTES
MARC GUIU: Came on to boost the frontline but did very little. 5
MARC CUCURELLA: Made Chelsea look a better side when he came on but did nothing hair-raising. 6
DARIO ESSUGO: Unlike the man he replaced, the substitute was positive and put in a great cross for Garnacho goal. 6
JOAO PEDRO: Chelsea were desperate not to go out of the FA Cup and his introduction and goal proved just that. 7
MALO GUSTO: Did an interview recently saying he wants to be best right-back in the world. He's got some work to do on that score, giving away a needless free-kick on the edge of the box. 5
JESSE DERRY: One of six substitutes as Chelsea changed things around. 5