Croatia international Kalinic broke his Atletico duck in Wednesday's 4-0 Copa del Rey win over Sant Andreu and his 25th-minute strike was added to late on by Griezmann and Rodrigo to send the hosts joint-top of LaLiga with Barcelona.
With Costa anticipated to be out for two months following foot surgery, goals from Kalinic and Griezmann will be a huge boost for Diego Simeone, though a first-half injury for Lucas Hernandez will provide cause for concern.
Atletico had to weather a difficult second half against their persistent visitors, but Griezmann and Rodrigo struck in the 82nd and 87th minute respectively to seal the win by a flattering scoreline.
Thomas Lemar's introduction spurred Atletico on to their win over Sant Andreu and after he spread the play out to Santiago Arias, the Colombian whipped in a cross that Kalinic diverted home with his stomach.
4 - Atletico have scored a goal in the first half in a LaLiga game after four games without doing so. Return. pic.twitter.com/euFjsWjpJi— OptaJose (@OptaJose) December 8, 2018
Ibai Gomez warmed the gloves of Jan Oblak from 20 yards in response and the hosts lost Lucas nine minutes before the break after Jonathan Calleri landed on his leg following an aerial challenge.
Jose Gimenez returned after a month out with a hamstring issue to replace Lucas and he hit the post from Lemar's corner three minutes after the restart.
Alaves continued to provide a threat against their stoic hosts but Griezmann put the game to bed when he tucked home from an acute angle after a challenge from Victor Laguardia pushed his initial attempt against the post.
Rodrigo rounded things off for Atletico five minutes later, tapping home from close range after Fernando Pacheco had kept out a powerful effort from Angel Correa.
What does it mean? Alaves a serious contender
This fixture would not have been tipped as a top-four contest prior to the start of the season, but Abelardo's excellent Alaves side proved they are worthy of their place in LaLiga's upper echelons. The visitors showed great levels of confidence to keep the pressure high against the division's best defensive side, but they were caught short at the back in the closing stages and punished by the title hopefuls.
Kalinic repays Simeone faith
Simeone told the media on Friday he did not anticipate Atletico signing a new striker in January following Costa's foot surgery. After a slow start since moving to Madrid from AC Milan, Kalinic added some weight to his coach's words with his second goal in the space of four days. His withdrawal early in the second half suggests he can expect to see a decent chunk of minutes in the Champions League next week.
Oblak gets uncharacteristically edgy
He may have only conceded 10 goals in LaLiga this season, but Oblak had some worrying moments as Alaves asserted themselves in the second half. The Slovenia international displayed a lack of conviction when coming for a number of crosses, flapping at a couple and pushing one that was clearly going wide without an Alaves player nearby out for a corner.
Key Opta Facts
- Griezmann scored his first LaLiga goal against Alaves in his third appearance against them; he has only failed to score in the competition against Atletico (eight games played) and Mallorca (six).
- Rodrigo has scored two goals in his last four LaLiga appearances, twice as many as he managed in his previous 71 games in the competition.
- Atletico have only lost one of their last 29 LaLiga home games (W20 D8), a 0-2 defeat against Espanyol in May.
Atletico will look to wrap up top spot in Champions League Group A during their trip to Club Brugge on Tuesday, while Alaves entertain Athletic Bilbao a week on Monday.