Forward Gareth Bale, who made his first La Liga start on Sunday night since September after getting through both calf and hamstring difficulties, scored twice for Real. But Celta drew thanks to goals from Daniel Wass and Maxi Gomez, reports Efe.
In Barcelona, two first-half goals from Argentine star Lionel Messi and Uruguay's Luis Suarez as well as a last-gasp goal by Brazilian Paulinho, earned the hosts their 15th league win.
Barcelona, who have 48 points, enjoy a nine-point lead over second-placed Atletico Madrid.
Although Real Madrid have a game in hand, the capital club now trails Barcelona by 16 points. They have work to do to keep in touch with second and third placed Atletico Madrid and Valencia (37 points), who won their respective home games on Saturday.
Zinedine Zidane-coached Real showed clear signs of lack of motivation. Hosts Celta got on the board first in the 33rd minute on Wass' chip over goalkeeper Kaylor Navas, who was out of position.
Real equalised just three minutes later on a shot by Welsh forward Bale, who then swooped in for another goal two minutes after that.
The host team had a great chance to get back to even when Costa Rican Navas conceded a penalty in the 72nd minute, but the custodian managed to make up for his mistake by saving lago Aspas' spot-kick.
Celta continued to battle as the minutes ticked away, however. And finally it was Maxi Gomez who settled the final result after moving through a lax Madrid defence to blast in a header eight minutes before the final whistle.
Talking about the title challenge, Zidane said: "If we lose points every week, we can not get close. You have to go match by match."
Barcelona showed in their game against Levante that they are best placed to regain the title. They went at full steam in the first half, but eased the pace after the break.
Coach Ernesto Valverde decided to put French winger Ousmane Dembele into the starting line-up for the first time since September 2017.
Dembele joined Messi and Suarez on the attack, while Spanish veteran midfielder Andres Iniesta also returned to the starting line-up at the Camp Nou stadium. Iniesta made his 650th appearance for the Catalan club.
Messi, who was appearing in his 400th La Liga match, gave Barcelona the lead in the 12th minute, making the most of Jordi Alba's header with a close range shot at the right post.
Dembele and Suarez squandered a double chance in the 25th minute, while Messi's free kick touched the woodwork on its way out in the 32nd minute.
Another back-forward duo proved decisive for Barcelona on the second goal as right-back Sergi Roberto assisted Suarez doubling Barcelona's lead in the 38th minute.
Ivan Rakitic, Messi and Paulinho all squandered scoring chances during the next few minutes before the break.
The Catalan club seemed to have run out of steam in the second half.
Barcelona's German goalkeeper Marc Andre Ter Stegen saved scoring chances from Ivan "Ivi" Lopez and Shak Moore in the 47th and 67th minutes.
In the last few minutes of play, Barcelona sought a third goal, with Suarez missing on a close scoring chance. But three minutes into the second half stoppage time, Paulinho tapped in a Messi cross from the left to make it 3-0.
Meanwhile, Athletic Club Bilbao enjoyed an easy 2-0 win over Alaves thanks to a first half goal from Xabi Etxeita and a 67th-minute penalty from Aritz Aduriz.
Leganes kicked off 2018 with a 1-0 win at home to Real Sociedad thanks to a 75th-minute goal from Gabriel Pires' free-kick against a rival which controlled much of the ball but failed to create clear chances.
Finally, goals in the 73rd and 77th minutes from Fabian Orellana and Sergi Enrich saw Eibar ruin Paco Jemez's debut for Las Palmas, who had opened the scoring with a Jonathan Viera penalty.
(This story has not been edited by Social News XYZ staff and is auto-generated from a syndicated feed.)
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