Pacheco made a decent save to prevent a Nacho header finding the back of the Alaves net in the 31st minute, but the home side were causing problems down the other end, with a succession of crosses into the Real Madrid box forcing Casemiro and Varane to both make brilliant clearances.
Real had the chance to extend their lead in the 55th minute when Isco through on goal, but the midfielder failed to convert past Pacheco.
Perhaps a matchup with Alaves is just what the doctor ordered-Alaves has lost all five of its La Liga games on the season and have not scored a goal on the season.
Real skipper Sergio Ramos, who had a header disallowed, missed an open goal from eight yards.
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Yet, Alaves could also have snatched a first point of the season as Alfonso Pedraza's deflected effort hit the bar before Pedraza struck the post when clean through on goal.
Zinedine Zidane's charges did push for another goal but they were unable to carve out another chance and had to settle for a 2-1 win.
"We are happy that a player of his stature wants to come to Atletico Madrid", Atletico boss Diego Simeone said of Costa's return.
Ceballos received a pass from Marco Asensio, fought through a tackle, and shot just inside the post for the opener.
However, a combination of poor finishing, bad luck and good saves from Betis keeper Antonio Adan kept them at bay as they laid siege to the Betis goal in the second half and Zinedine Zidane's side were caught by a sucker punch by the Paraguayan, who moments earlier had seen a goal correctly ruled out for being offside.