Antoine Griezmann and Rodrigo Riquelme scored a goal in each half for Atletico, who lie fifth in the table with a game in hand over the sides above them.
Atletico beat Madrid 3-1 at home on Sunday, with France international Griezmann scoring one of the goals for Diego Simeone's team.
"It was important not to get caught up with what happened against Real Madrid and to come here to win," Griezmann said.
"We are improving and we have to keep working to keep improving."
Griezmann opened the scoring with a shot from a tight angle in the 20th minute, and Riquelme sealed the victory with a breakaway goal in the 81st, shortly after Osasuna had an effort disallowed because of a controversial foul on a defender inside the area.
Osasuna coach Jagoba Arrasate was sent off for complaining about the referee's decision.
Both teams played the last five minutes with 10 men after Osasuna's Chimy Avila and Atletico's Alvaro Morata were sent off following an altercation.
The result extended 14th-placed Osasuna's winless streak to five matches in all competitions.
Real Betis's winless run reached four matches in all competitions with a 1-1 draw at second-to-last-place Granada.
Assane Diao put the visitors ahead in the 51st minute before Granada's Lucas Boye equalised in the 67th.
Celta Vigo remain on the edge of the relegation zone after a 1-1 draw at home against Alaves.
The hosts opened the scoring with an own-goal by Rafael Marin. Alaves levelled through Samuel Omorodion midway through the second half.
Celta, who did not register a single shot on target, played with 10-men after Luca de la Torre was sent off in the 68th.
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