Eibar went ahead in the 20th minute with a strike from Barca's on-loan midfielder Marc Cucurella which squirmed under keeper Jasper Cillessen but Messi levelled in the 31st after sneaking into the box to meet a pass from Arturo Vidal.
Messi struck again a minute later, racing through the middle unchallenged to latch on to a pass from Ivan Rakitic and calmly chip the outstretched keeper Marko Dmitrovic.
But Eibar's Pablo de Blasis levelled right before halftime with a superb one-touch strike from long range after the ball fell into his path following a desperate header away from Cillessen, who looked in shaky form ahead of next week's Copa del Rey final against Valencia.
Malcom and Gerard Pique missed second-half chances for the champions while Cucurella spurned an even better opportunity to snatch a winner for Eibar, who have still never managed to beat Barca in the top flight.
Messi had a difficult chance to score again and complete a hat-trick but sent his shot well over the bar.
The Argentine still finished the campaign as La Liga's top scorer for a third year in a row, the first player to do so since Hugo Sanchez of Real Madrid in 1987.
He also joined the late former Athletic Bilbao striker Telmo Zarra as the only players in the league's history to be top scorer six times.
Messi scored 15 goals more than his nearest challengers, Barca team mate Luis Suarez and Real Madrid's Karim Benzema who both netted 21 times.
Barca, who clinched an eighth title in 11 seasons with three games to spare, finished the campaign on 87 points, 11 clear of runners-up Atletico Madrid and 19 ahead of Real Madrid in third.
Their focus now turns to beating Valencia in next week's Cup final in Seville to complete a second consecutive domestic double.
Their season, however, is still likely to be overshadowed by their Champions League semi-final elimination to Liverpool.