Real make easy work of Celta
Argentinian striker Higuain gave the current La Liga champions the lead on 12 minutes before Ronaldo wrapped up the points with a second-half penalty for a Real side that never really got going against unambitious opposition.
Newly-promoted Celta, backed by noisy support, had won on their last two visits to the Santiago Bernabeu in 2004 and 2007 but never looked like repeating that feat this time.
Coach Jose Mourinho needed to shuffle his pack after a number of players returned with injuries from international duty. Brazilian international Kaka was called to start his first league game of the season, while Raphael Varane took over in the centre of defence for only his second.
There was also room for recent signings Michael Essien and Luka Modric as Mourinho kept one eye on Wednesday's UEFA Champions League tie at Borussia Dortmund.
It was Sergio Ramos, filling in at right-back, who had the first chance of the game when he headed a corner just over on three minutes, and from that point a pattern of Real dominance was established.
By the 12th minute Real were ahead when Higuain powered down the left wing and hit what looked like a cross that curled into the top far corner. Ramos almost made it two from close range and then Ronaldo headed over a cross from Higuain as Celta struggled to get into Real's half.
On 25 minutes they did mount their first attack when the impressive Iago Aspas forced a way through the home defence and produced a diving save from Iker Casillas.
The visitors were showing more signs of life with some neat passing but Real continued to look comfortable and could have doubled their lead on 37 minutes when Ronaldo clipped the bar with an inventive volley.
Ronaldo wraps it up
Unhappy with only the one-goal advantage at the interval, Mourinho called time on Kaka's return by replacing him with Angel Di Maria for the second period.
The half began at a slow pace until the 61st minute when Essien burst down the left flank and Ronaldo narrowly headed wide his cross. Next it was Varane's turn to head wide from a corner and Real's anxiety was increasing as time ticked by with the single-goal lead.
But when Mesut Ozil went down under a challenge from Gustavo Cabral on 68 minutes, Ronaldo made no mistake from the spot to make it nine league goals for the season, one more than Lionel Messi and Radamel Falcao.
Substitute Jose Callejon forced a save from Celta's reserve goalkeeper Sergio Alvarez and Quique de Lucas did the same at the other end for the visitors. Casillas was forced into another save from a Chu Young Park header before the game petered out with both sides seemingly content with the result.
Real's assistant coach, Aitor Karanka, expained the side's gameplan afterwards. "We knew if we let them have the ball they would give us problems because they can play good passing football, so we went out to pressure them and not let them settle down to their usual game," he said.