Brazilian forward Costa was suspended for Atletico's last two games, against both Rayo Vallecano in La Liga and Rubin Kazan in the Europa League, both of which ended in defeat.
Atletico boss Diego Simeone backed Costa to help his side snap their poor form on his return and he duly delivered, his well-taken second-half goal adding to Radamel Falcao's early opener.
Cristian Rodriguez added a late third as Atletico won on the road for the first time since November 18 to close back to within 12 points of leaders Barcelona.
Second-placed Atletico had won just two of their last six games in all competitions heading into tonight's contest but never looked in any danger of ending with anything other than all three points as Valladolid turned in an abject display.
The hosts failed to muster a shot on target over the 90 minutes and they may yet be eternally grateful for the current 10-point gap they enjoy above the relegation zone if performances continue in a similar vein.
Atletico wasted little time in taking the lead, just 10 minutes on the clock when Falcao netted his 23rd of the season, although the Colombian was lucky to be given the benefit of the doubt in a close offside call.
Omar created the opening as Diego Godin latched on to his free-kick to fire an effort that Daniel Hernandez could only parry, and Falcao was in the right place to bundle the ball home.
Atletico were good value for their lead and Costa might have made it 2-0 at the break but his lobbed effort was saved by Hernandez.
Costa did make it two just eight minutes into the second half, the forward played in by Jorge Koke's cute header and he finished low and hard beyond the goalkeeper.
As Valladolid's lamentable efforts up front continued, coach Miroslav Djukic threw on Angola striker Manucho to add a bit of muscle, but the change did little to affect the course of the match as Thibaut Courtois remained a spectator in the visitors' goal.
The visitors' victory was cemented in the final minute as a defensive blunder allowed Rodriguez to add a third, the substitute gleefully poking the ball home from close range after Antonio Rukavina's attempted chest back to his goalkeeper fell short.