Diego Simeone's side trailed 1-0 in the 83rd minute at Estadio Principe Felipe, after Alvario Merencio's first-half strike.
However, the LaLiga side levelled through Clement Lenglet, before striking twice in stoppage time through Julian Alvarez and an Adri Perez own-goal.
Julio Cobos' side were on a four-match winning streak in Group 5 of the Segunda Federacion, and took the lead on the half-hour mark, with Merencio rounding off a quick counter.
The hosts held firm but were finally breached seven minutes from time, when Lenglet headed in from Rodrigo de Paul's cross.
Cacereno were reduced to 10 men two minutes later with Jaime Sancho shown a second yellow card, and Atletico capitalised on their numerical advantage in stoppage time.
De Paul's shot deflected in off Perez to complete the turnaround, while Alvarez put the tie beyond the fourth-tier outfit later on.
Data Debrief: Late, late show spares Atletico blushes
Atletico had won each of their last seven matches across all competitions, but they were given an almighty scare on Thursday.
Nevertheless, Simeone's side eventually broke Cacereno's resistance, scoring three goals from the 83rd minute onwards in any competition for only the second time - also doing so against Real Zaragoza in June 2013.
Le Normand had not played since his side's 1-1 draw at home to city rivals Real Madrid in September, in which he suffered a severe head injury following a collision with Aurelien Tchouameni and required extensive treatment on the pitch.
Thursday's match against fourth-tier opposition was his ninth appearance since joining the club from Real Sociedad in the summer and Simeone was pleased to see the Spain international back on the pitch.
"We are very happy that he is back with the team," Simeone said.
"It is normal that he needs that time to get back to playing, he will need that time playing, training and competing to be at his best. We are waiting for him and we need him, he is a very important player for us."
The match itself was not as straightforward as Atleti would have liked, having gone a goal down after half an hour.
It took an 83rd-minute Clement Lenglet goal to draw level before an effort from Julian Alvarez and an Adri Perez own-goal in stoppage time secured Atleti's passage through to the next round.
Having taken until the 81st minute to get ahead in their 2-0 victory over sixth-tier Vic in the previous round, Simeone explained he had been expecting it to be a tough test.
"We had been through it with Vic. They are not easy, Girona, Villarreal, Espanyol have been eliminated. It is not easy. The teams have enormous enthusiasm, they work together as a team, they get a goal that raises their enthusiasm. It is not easy to keep it up until the end," he said.
"The game was as expected, a great cup game, with a very hard-working opponent. When you show little decisiveness you run the risk of losing. We have to improve in that part."
