The France striker’s goals were both assisted by Germany midfielder Toni Kroos as Madrid moved above rivals Barcelona into second in the table.
Celta pulled one back on 40 minutes through Santi Mina’s powerful header.
After a lethargic second half from Real, Benzema turned provider as Marco Asensio added a third in stoppage time.
Benzema’s double at the Balaidos puts the 33-year-old on 23 goals in all competitions for Madrid so far this season.
Real’s victory also edges Zinedine Zidane’s side to within three points of league leaders Atletico Madrid, as the French boss continues his quest to lift back-to-back titles with the Spanish giants.
Atletico and Ronald Koeman’s Barca play their league games on Sunday.
With nine games to go until the end of the La Liga season, Benzema has hit a purple patch at just the right time.
His strike against Atalanta on Tuesday gave Real the platform to secure a 4-1 aggregate win that put them through to an eye-catching Champions League quarter-final against Premier League champions Liverpool.
In Saturday’s encounter with Celta Vigo, Benzema first latched on to Kroos’ threaded pass to turn his marker and clinically finish into the bottom corner past goalkeeper Ivan Villar.
His second – and eighth in six matches – was a left-footed shot driven home after midfielder Kroos dispossessed defender Renato Tapia on the edge of the Celta penalty area.
Benzema’s assist for Asensio’s late, close-range shot was checked by VAR for offside, but the strike was awarded on the full-time whistle.
There were good and bad points for Zidane to ponder after Madrid’s second win in a week.
His side are now unbeaten in 10 away games in La Liga but have not kept a clean sheet in their last four league games.
It was also a nervy second 45 minutes for Real, as former Liverpool striker Iago Aspas twice came close to finding an equaliser for 11th-placed Celta.
The Spaniard saw an effort palmed away by Madrid keeper Thibaut Courtois, then a thunderous free-kick deflected off the head of Casemiro and hit the post.
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