A thrilling contest ended in a 3-3 draw, before extra time and penalties were needed at the STok Cae Ras.
The Reds were 2-0 up at the break through Liberato Cacace (37′) and Ollie Rathbone (40′).
Forest then pulled one back through Igor Jesus (64′) before a Dominic Hyam goal on 74 mins looked to have sent Wrexham through.
But a Callum Hudson-Odoi double (76′, 89′) sent the tie to extra time.
After a goalless two-halves there, it was time for penalties. And it was Wrexham who came out on top 4-3 after goalkeeper Arthur Okonkwo denied both Omari Hutchinson and Igor Jesus from the spot.
One half of Wrexham’s star ownership was also in attendance at the match as Ryan Reynolds cheered the Reds on from the stands and also greeted fans and players pre-match.
Other fans were spotted pumping themselves up for the game at The Turf pub, which lies in the shadow of the football ground.
Wrexham now have to wait and see who they draw in the next round of the cup with other matches being played today, tomorrow and Monday (January 12).
So, in the meantime, enjoy the gallery of pictures above taken by the Press Association.