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Four wins in 11 league games had seen Atletico's 10-point advantage in February reduced to one before this weekend, with Real Madrid and Barcelona threatening to overtake the leaders during the run-in.
But a thumping victory over struggling Eibar may prove the spark to turn Atletico's form around while also putting pressure on Real Madrid, who play at Getafe later on Sunday.
Fourth-placed Sevilla, six points adrift, could yet join the race after they defeated Real Sociedad 2-1 earlier on Saturday.
Barcelona, who beat Athletic Bilbao to win the Copa del Rey on Saturday, are five points off the top, with their next game on Thursday at home to Granada.
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Atletico's problems were deepened by an injury to their top scorer Luis Suarez earlier this month but Marcos Llorente and Angel Correa filled the void, both scoring twice either side of Yannick Carrasco making it three just after half-time.
It is the first time Atletico have scored five goals since they hammered Cadiz back in September, a comfortable win appearing almost cathartic for a team that have struggled so much for goals in recent weeks.
Eibar, who stay rooted to the bottom of the table, were perhaps the perfect opponents for the start of a recovery but games against Huesca, the out-of-form Athletic Bilbao and Elche should now offer Atletico a chance to regain momentum before a crunch trip to Barcelona on May 8.
Atletico scored four goals in 11 minutes either side of half-time, with Correa finding the net in the 42nd and 44th minutes, first prodding in at the back post before twisting on Carrasco's pull-back to make it two.
Carrasco then scored himself four minutes after the interval, sent clear by Saul Niguez's ball over the top and poking it through the goalkeeper's legs to finish.
It was four in the 53rd minute, as Saul Niguez sprayed a pass left to Renan Lodi before Correa found Llorente in the box and he had time to turn and pick his spot.
The excellent Llorente started and finished the fifth, combining quickly with Lodi and Carrasco again before firing in his second and sealing an emphatic win.
Earlier in the day, Julen Lopetegui's Sevilla came from behind to stay in touch with the leading trio.
Carlos Fernandez gave Sociedad a fifth-minute lead, but first-half goals from Fernando and Youssef En-Nesyri, his 16th in the league this season, secured Sevilla a third straight win.
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