After an unusually quiet first 45 minutes, Messi burst into life after the restart and claimed his milestone goal – his 13th in eight appearances against Eibar.
Luis Suarez had given Barca the lead with its only shot on target in the first half, and he doubled his tally six minutes after Messi's moment in the spotlight with a composed finish from a tight angle.
That was enough to seal a sixth win in a row for Barca in the league, and a ninth successive over Eibar since its promotion to the top flight.
Messi took up more of a playmaker role in the opening exchanges and created half-chances that Gerard Pique and Jordi Alba were unable to convert.
Suarez showed them how it should be done in the 19th minute after a slick interchange with Philippe Coutinho opened up the Eibar defence, the Uruguay international finding the bottom corner with unerring accuracy.
Despite falling behind, Eibar continued to push forward and Sergi Enrich should have done better from Ruben Pena's cross, however the striker headed wide of Marc Andre ter Stegen's goal.
Coutinho felt he should have had a penalty minutes before the break but his claims were waved away despite Pena's clumsy tackle inside the area.
After the lacklustre opening salvo, Barca had much more urgency to its game after the break and eight minutes into the second period Messi got his landmark goal.
Having received the ball from Suarez, the five-time Ballon D'Or winner made himself some space before firing low under Asier Riesgo.
Suarez then notched his 14th league goal of the campaign to extend Barcelona's advantage, before Ter Stegen needed to be alert to keep out Pablo De Blasis' close-range header.
Ernesto Valverde introduced reported Manchester City target Ousmane Dembele with 18 minutes to play, but despite looking lively he was unable to stretch Barca's lead on what ultimately turned out to be a comfortable victory despite the league leader being far from its fluent best.