Thomas Lemar scored the 85th-minute winner for Atletico, ahead of Barcelona’s game against Real Sociedad later Saturday.
The victory left Atletico seven points clear of third-place Real Madrid, which hosts Athletic Bilbao on Sunday.
Diego Simeone’s team is looking to finish runner-up for the second straight season. Before winning the league in 2014, Atletico hadn’t finished better than second since 1990-91.
It got the win over Eibar despite playing without suspended forwards Diego Costa and Antoine Griezmann. Costa is out for the season after being handed an eight-match suspension for insulting a referee in a loss at Barcelona two weeks ago.
Atletico struggled to take control of the match at Ipurua Stadium, unable to create many significant scoring chances until Jorge “Koke” Resurreccion broke free and sent a perfect cross for Lemar’s close-range shot by the far post.
“It’s always difficult to play here,” Koke said. “We are glad we were able to win the match. We got the three points and we’ll keep fighting until the end.”
It was the fourth win in five matches for Atletico, with the only setback being a loss against Barcelona at Camp Nou Stadium two weeks ago.
Eibar, which has won only one of its last seven matches, stayed 13th in the 20-team standings after 33 matches.
Celta Vigo took a step toward escaping relegation with a 2-1 home win over Girona.
Sofiane Boufal netted the 69th-minute winner for the hosts, which had opened the scoring with Iago Aspas in the 34th before Portu equalized for Girona in the 48th.
The win moved Celta to 14th place, three points from the relegation zone.
Girona, which has lost five straight in the league, dropped to 15th, two points from safety. Its next match is at Valladolid, the first team currently inside the relegation zone.