The Real Madrid star also boasts 110 in the Champions League alone, against Messi's 97, although he has also played 143 games compared to Leo's 118 (excluding qualifiers).
However, the opposition appeared to be given a way back into the game just before half-time when Pique was sent off for two yellow card offences.
Moments after Paulinho blasted a shot just over, Nikolaou miscued his clearance on the end of Deulofeu's cross, diverting the ball into his own net to give the Blaugrana the lead.
Proto found himself in no-man's land midway through the half when Paulinho latched on to Andres Iniesta's chipped pass forward, but Olympiacos were saved by the woodwork as the Brazilian's header came back off the crossbar with the keeper beaten.
However, Barcelona continued to outclass Olympiakos despite playing with 10 men.
Olympiakos remained with zero points.
Suarez missed a second great chance of the game after being played in by Messi on 33 minutes, but Proto denied him with an impressive save.
Instead of having his own "Hand of God" moment, the referee showed Pique a yellow card. Messi hit the century mark in 122 European matches when he scored from a free kick in the 61st minute.
Dimitris Nikolaou, whose own-goal let Barca open the scoring, scythed Messi down on the edge of the area and Olympiacos goalkeeper Silvio Proto could not prevent him making it 2-0, parrying a curling effort into the roof of the net.
Valverde's side are now six clear of third place, though, and could seal a place in the last 16 for the 14th season in a row should results go their way when they meet Olympiacos again in a fortnight's time.
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