The Germany international left it late to secure three points to keep the club's incredible winning Liga run going, after Fabian Orellana had levelled with a stunning shot.
Toni Kroos made the difference for Real Madrid just 10 minutes from the end to end Celta's hopes of a share of the points, as the hosts prevailed 2-1 at Santiago Bernabeu.
A quiet game burst into life in the final 30 minutes, with Alvaro Morata giving Madrid the lead, only for an excellent strike from Fabian Orellana to set up a tense finish.
But Madrid were not to be denied, with Kroos striking from outside the area with just nine minutes left to delight the Santiago Bernabeu.
Following the win, Zinedine ZIdane's men have six points from their first two games, with title rivals Barcelona facing a testing trip to play Athletic Bilbao on Sunday.
Madrid have now won 14 league matches in a row and will have the chance to match their record of 15 – set in 1961 – when they play Osasuna after the international break.
The home side won last season's fixture 7-1 in March, but goals were not flowing as freely without injured attacking duo Cristiano Ronaldo – who scored four in that game - and Karim Benzema.
Indeed, it was Celta who could have taken the lead midway through the first half when Theo Bongonda sliced wide from a decent opening.
Zidane's men upped the pressure as the opening period progressed, with Luka Modric - who had earlier tested Sergio Alvarez – so unlucky not to score after surging forward and seeing a stunning, curling strike bounce away off the crossbar.
Modric forced Alvarez into a good diving save with his third effort, before Gareth Bale headed a good chance wide from Kroos' corner.
Bale was first to threaten in the second half as his dipping free-kick clipped the top of the bar.
The breakthrough arrived on the hour mark when Alvarez's poor clearance gave Modric the chance to run into the box and send a pass into the area. The goalkeeper thought he had atoned for his error by saving from Marco Asensio, but Morata was there to smash home the rebound with his left foot.
Morata came so close to a second on the counterattack moments later, seeing his deft shot hit the foot of the post after Kroos had superbly launched the move.
The failure to convert that chance then proved costly after 67 minutes as John Guidetti found Orellana 20 yards out and he picked his spot with curling shot into the far corner.
Substitute James Rodriguez and Marcelo both had penalty appeals denied as Madrid searched for a late winner, while Alvarez got down to keep out Bale's header.
Just as it looked like Madrid were going to have to settle for a surprise draw, the winner arrived.
Lucas Vazquez, who had come off the bench, made ground down the right and cut back for Kroos and the Germany international guided a controlled low strike in off the post from 20 yards to keep the streak alive.
