With Xavi Hernandez set to take over as Barca's new coach next week, interim boss Sergi Barjuan looked set to sign off with a win thanks to first-half goals from Ansu Fati, Sergio Busquets and Memphis Depay.
Frenkie de Jong struck the bar late on and Barca looked on course for three points until Aspas' brilliant effort from the edge of the box in the last minute of the game.
Nico was sensational in midfield before being forced off with an injury. The 19-year-old has produced some stunning performances in recent weeks.
The injuries and the collapse. Barca were already missing Neto, Gerard Pique, Sergino Dest, Sergi Roberto, Pedri, Ousmane Dembele, Martin Braithwaite and Sergio Aguero for this game. Ansu, Garcia and Nico have now all joined them in the treatment room. Ansu hurt his hamstring and Garcia his calf, while Nico also seemed to pick up a muscle injury. Luckily, there's an international break now.
Despite that, the collapse should not be forgiven. Barca still had a centre-back pairing of Ronald Araujo and Clement Lenglet on the pitch, with experience from the likes of De Jong, Busquets and Jordi Alba. They should have gotten over the line.
Manager ratings out of 10
5 -- Barjuan can't be blamed too much. Not only has he had very little time to work with the team, he also has been handed a side with serious injury problems.
Player ratings (1-10; 10 = best, players introduced after 70 minutes get no rating)
GK Marc-Andre ter Stegen, 4 -- Fumbled the cross, which led to Aspas' goal in the second half.
DF Oscar Mingueza, 5 -- Celta created problems down the Barca right in the second half, with Mingueza lucky not to give a penalty away at one point.
DF Eric Garcia, 6 -- Booked in the first half before coming off with a calf problem, which might force him to pull out of the Spain squad.
DF Clement Lenglet, 5 -- Produced a great block to keep out Renato Tapia, but lost his way as Celta poured forward. Lost track of Nolito for the second goal.
DF Jordi Alba, 6 -- Brilliant cross to set up Memphis' goal, but struggled defensively in the second period.
MF Sergio Busquets, 5 -- Took his goal well from 18 yards. It was just his 16th in almost 650 appearances for the club. Lost the ball in the buildup to Celta's second goal.
MF Nico Gonzalez, 8 -- Was brilliant, which made his injury feel even more cruel. Strong and technical, he set up the second goal and played a key role in the third.
MF Frenkie de Jong, 6 -- Had good moments driving forward with the ball, one resulting in a chance for Ansu and another in the him smashing the crossbar late on.
FW Gavi, 6 -- Worked hard and was especially effective in defence, despite playing wide right rather than his preferred central role for the second game running.
FW Memphis Depay, 6 -- Headed in Barca's third, his sixth of the season, but didn't keep the ball well enough in the second half as the Blaugrana tried to protect their lead.
FW Ansu Fati, 7 -- Has a knack for opening the scoring. Of his 17 goals for Barca, 11 have been the first of the game. Unfortunately, had to go off injured before the break.
FW Alejandro Balde, 5 -- The teenager was thrown on for Ansu but looked his age as Celta roared back.
DF Ronald Araujo, 5 -- Couldn't clear the ball after ter Stegen's fumble or prevent Celta's comeback after replacing Garcia at the break.
MF Riqui Puig, 5 -- Lost the ball too much after coming on for Nico. Sent a couple of speculative efforts off target.
FW Abde Ezzalzouli, NR -- The B-team winger looked dangerous running with the ball but didn't produce too much in the final third.