It is the first time since 2000 that the Welsh outfit have went beyond the third round as they edged out a seven-goal thriller at the CBS Arena.
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In what proved to be a crazy game, National League side Wrexham almost threatened to throw away the match after leading 4-1.
Championship outfit Coventry closed the gap to 4-3, but failed to score an equaliser in what proved to be a huge FA Cup shock.
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Wrexham raced into a 2-0 lead after just 18 minutes thanks to goals from Sam Dalby and Elliot Lee.
It led co-owner Ryan Reynolds to post an X-rated message on his Instagram story from inside the ground.
It simply read: "What the f*** is happening?"
Ben Sheaf then pulled a goal back for the hosts, before Thomas O'Connor restored Wrexham's two-goal lead in first half stoppage time.
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And the travelling fans were sent into ecstasy in the 58th minute after Paul Mullin scored from the penalty spot.
Wrexham looked to be home and dry in securing their spot in the fourth round, only for Coventry to reply with two quickfire goals.
Viktor Gyokeres pulled a goal back in the 69th minute, before Kaskey Palmer closed the gap to just a single goal shortly after.
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But Wrexham showed their resilience in fending off late pressure from Coventry, who had been playing with ten men since the 57th minute after Jonathan Panzo was sent off.
Wrexham have enjoyed a fantastic 2022/23 season so far since enduring heartbreak in the National League play-offs last season.
They sit second in the table - five points behind leaders Notts County, though they do have two games in hand over them.
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Taking to Twitter after the match, Reynolds said: "I'm completely and totally speechless.
"What a club. What a town. What a win. Wrexham forever."