The World Player of the Year converted a penalty in the 24th minute to claim a double century of goals for Barca after being felled by defender Marian Cisovsky who got a straight red card.
Messi fired home a second from close range in first-half stoppage-time and, after Cesc Fabregas got on the scoresheet late on, the Argentine scored his hat-trick, and Barca's fourth goal, in added-time at the end of a game they dominated.
"I am happy but more than anything for the result," Messi said in a pitchside interview with Spanish television, adding that he was not thinking about catching the Catalan club's record marksman Cesar Rodriguez, who scored 235.
Barcelona coach Pep Guardiola added: "Messi is a phenomenal player, what more can I say."
Czech league champions Plzen started brightly and could have taken an early lead after Milan Petrzela's shot was turned away by Barca keeper Victor Valdes.
The tide turned after the penalty and Plzen spent the rest of a chilly night struggling for possession.
Plzen coach Pavel Vrba rued his team's failure to score when given the chance and the red card which left them facing a mammoth task for the rest of the night.
TWO INCIDENTS
"Two incidents decided the game," he said. "Milan Petrzela had the clear chance but failed to score and then the penalty and the red card came."
"We wasted the chance before the first goal but we are not used to the high pressure in our domestic league like Barcelona."
Messi opened the scoring from the spot before grabbing his second after a nifty one-two with Adriano on the edge of the box and scored his hat-trick after rounding the keeper and slotting into an empty net for his 202nd goal for the Catalan side.
Thiago Alcantara nodded against the bar from Messi's cross midway through the second half before Fabregas headed in the third after 72 minutes from a cross by striker Issac Cuenca, who was making his first appearance in the competition.
Milan's 1-1 draw at BATE Borisov earlier on Tuesday means Barca are assured of at least second place in Group H with two games left. Milan are also through to the knockout rounds because they have a better head-to-head record over BATE.
Barcelona are top on 10 points from four matches, with Milan second on eight points. BATE have two and Plzen one.
Keeper Valdes set a Barca record for minutes unbeaten late in the first half when he reached 825 without conceding a goal.
That bettered a mark held by Miguel Reina, father of Liverpool goalkeeper Pepe, since the 1972/73 season.
