On the face of it, this looked like a tricky away trip for Real and so it proved to be in a high-energy encounter at the Estadio de Balaidos.
Gareth Bale arguably should have done better early on as he attacked Marcelo’s cross from the left, before Cristiano Ronaldo saw a low effort easily saved by Ruben Blanco in the home goal.
At the other end, Iago Aspas got caught in two minds when played in on the left and opted to look for a pass that wasn’t on, rather than go himself.
Aspas went even closer with 13 minutes gone as he side-footed Hugo Mallo’s cross from the right against the near post after escaping the attentions of Real’s back-line.
Both sides looked at their most dangerous on the counter at this point, with Daniel Wass wasting a good chance after being teed up by Maxi Gomez, before Casemiro forced Ruben into a save with a long range strike.
What followed can only be described as ‘five minutes of madness’ as Celta took the lead, only to relinquish it in the blink of an eye.
First, Celta broke the deadlock thanks to a fine goal from Daniel Wass. The Dane was left all alone out on the right as Celta countered and Aspas picked him out with an precise ball. Wass drove into space, before dinking the ball over the head of a helpless Keylor Navas and into the back of the net from the edge of the box.
It was a fine goal, but before Celta had time to savour it they were picking the ball out of their own net.
Maxi Gomez squandered possession in a promising position and Real punished them. Toni Kroos picked out Bale with an inch-perfect through ball and the Welshman duly slotted past the onrushing Ruben to level things.
Not content with one goal, Bale completed his quickfire double just two minutes later as he escaped his marker to prod home Isco’s cross from deep.
Bale’s brace ensured that Real led at the half and it was the visitors who looked most dangerous early in the second period.
Isco called Ruben into action with an effort from range, before Ronaldo blasted wide after meeting Achraf’s low cross from the right.
Real almost caught Celta out with a quickly-taken free kick but Isco’s effort fizzed narrowly over the bar.
Aspas was at the heart of Celta’s best play all evening and his dogged work to keep possession allowed him to tee up Jony, but the defender fired inches over.
With 19 minutes to go, Celta were handed a way back into the game on a silver plate. Real were left exposed on the counter and Aspas was chopped down by Navas, leaving the referee no choice but to point to the spot.
Aspas assumed the responsibility, only to see his low effort brilliantly kept out by Navas down to his right.
Ronaldo wasted a chance to make the game safe on the counter as he fired straight at Ruben and Celta could have been forgiven for thinking that it wasn’t going to be their day. Those concerns disappeared into the Vigo air with 82 minutes played though as the hosts levelled.
Pablo Hernandez won the ball back in midfield and it was worked out to Wass on the right, whose cross was perfect for Maxi Gomez to plant a header past Navas from close range.
Both sides could have won the game from then on. Ronaldo lashed into the side-netting for Real, whilst Aspas was denied another penalty after going down under the challenge of Marcelo.
There was still time for Ruben to produce a fine save to deny substitute Lucas Vazquez's powerful volley as Celta held out for a well-deserved point.
The result leaves Real in fourth place in La Liga, 16 points behind leaders Barcelona after they beat Levante on Sunday afternoon, whilst Celta drop to 14th.