Matheus Cunha and Rodrigo De Paul were both on target as Atletico pulled six points clear of Real Betis in fifth, with two games left to play. Atletico also have a superior head-to-head record over Betis.
Sevilla, though, failed to make sure of their top-four spot as the team's poor end to the season had earlier continued with a goalless draw at home to struggling Mallorca.
Atletico look likely now to finish third and although the defence of their league title has been hugely disappointing - they are 14 points behind Real Madrid - Diego Simeone's side have at least avoided missing out on the Champions League, which for a while seemed a very real possibility.
In December, Atletico lost four league games in a row for the first time ever under Simeone, before defeat by Levante, who sat bottom of the table, prompted crisis talks between coach and players in February.
But five consecutive victories in March proved crucial and while there has been another dip in recent weeks, Atletico have done just enough to seal Champions League qualification for a 10th consecutive year.
Cunha gave Atleti the lead in the 28th minute as Antoine Griezmann picked out Renan Lodi's run down the left and Cunha was in the right place to divert in the cross to the near post.
The visitors made it two shortly after the hour, De Paul finishing off a superb move after a slick exchange with Lodi, who had again broken through the Elche defence.
Atletico play at home on Sunday to Sevilla, whose stalemate against Mallorca at the Ramon Sanchez Pizjuan should only delay their qualification given they sit five points clear of Betis, with two games left to play.
Sevilla will need only one more point to guarantee they finish ahead of Betis, as they also have the better head-to-head with their city rivals.
But Julen Lopetegui's side do have two tricky last games, with Sunday's trip to the Wanda Metropolitano coming before a final match at home to Athletic Bilbao.
And even if they get over the line, Sevilla are ending what was once a promising campaign with a whimper, after just three wins now in their last 12 in all competitions.
There were whistles from the home fans while Mallorca were hardly satisfied with a draw either. They stay 18th, two points adrift of safety, with Cadiz ahead of them playing a game in hand away at Real Sociedad on Thursday.
Sevilla had the better chances overall but Mallorca were far from overwhelmed and could have taken the lead on the break when Vedat Muriqi's header had to be clawed away by Bono.
Anthony Martial went close for Sevilla in the second half but their best chance came in injury-time as Youssef En-Nesyri connected well with a header, only for Mallorca goalkeeper Manolo Reina to make an excellent save.