The Argentina playmaker, though, then produced a trademark free-kick of his own to put Barca back in front heading into half-time.
Sergio Busquets added another in the 85th minute to complete the comprehensive win on the night.
As he took home another La Liga ball, this one would have felt special, as he has now equalled Ronaldo's record for the most hat-tricks scored in Spanish top-flight history. "Having him around gives us a real boost".
A second penalty, this time scored by Benzema just before the half hour, made it 3-0 and with the result already decided, Fede Valverde's first league goal for Madrid closed the scoring with just under half an hour left to play.
Despite going into the weekend within striking distance of top spot, the Catalans have had an uneasy campaign which hit a new low this week as players were booed off the pitch following the goalless draw at home against Slavia.
The defeat was Celta's fifth in a row and newly appointed head coach Oscar Garcia will have his work cut out as he tries to lift them out of the bottom three.
The visitors did well to contain Barca in the opening stages until Messi took advantage from the penalty spot but howls of frustration could be heard across the ground after Olaza's superb equaliser.
Messi was again Barca's savior and his contribution helped produce a score which flatters a side that struggled especially in the first half to produce the fluid football that has characterized their game over recent seasons.
"He dominates the art of free-kick taking, and opponents know they can not afford to give away fouls near our area".
Barcelona right-back Nelson Semedo became the latest player in the club to pick up an injury, as he suffered a calf problem and got substituted during their clash against Celta Vigo at the Camp Nou on Saturday.