Griezmann now has eight goals in as many games, his latest helping Atletico register their sixth win in seven league matches. The only dropped points came in a respectable draw away to Sevilla.
Saul Niguez tapped in a second before half-time at the Wanda Metropolitano to complete an impressively smooth victory over a Getafe side that had lost only once, to Barcelona, in 12 outings.
Renowned for their tenacity, Getafe strayed in the final minutes, when Djene Dakonam and Leandro Cabrera were both sent off.
"From the beginning of January the team has been playing well," coach Diego Simeone said. "We have injuries and I'm excited to think what we can do when they're all fit again."
"We were not good," Getafe coach Jose Bordalas said. "I didn't like my team, we weren't like us."
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Griezmann could have been playing for Barca had his decision been different last summer but instead he is fast-becoming the sharpest thorn in their side, driving Atletico almost single-handedly at times to a sustained title challenge.
Alvaro Morata could yet join this month, even if reports in the Spanish press have suggested a deal with Chelsea is proving difficult to close.
But with Griezmann in this sort of form and Diego Costa expected back next month, perhaps Atleti are less in need, with some fans even appearing to chant against Morata's arrival, although they were quickly drowned out by boos.
"The opinion is respectable, people can say what they want," Simeone said. "I look for players that serve the club and the team."
It is no coincidence that Griezmann's surge has coincided with a consistent run for Atletico, which looks timely too, with Real Madrid in La Liga and Juventus in the Champions League both to come at the start of next month.
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Simeone will hope the thigh strain that forced his captain Diego Godin off at the interval is not serious. Atletico described the substitution as a "precaution".
"He left with some discomfort," Simeone said afterwards. "Let's hope it's nothing."
Barcelona coach Ernesto Valverde had said earlier on Saturday that he considers Atletico the greatest threat to their title hopes from the Spanish capital and it is hard to argue given Simeone's side are now just two points behind, eight closer than Real Madrid.
Sevilla jumped above Real into third after earlier thrashing Levante 5-0, with all of their goals coming in the second half. Valencia move up to seventh after continuing their revival by beating Villarreal.
Barca and Real both have games in hand to come on Sunday, however, the former away to Girona and the latter up against Espanyol.
Atletico will watch on happy after Griezmann's shot in the 27th minute was too quick for Getafe goalkeeper David Soria. The excellent Thomas Partey had battled through midfield before teeing up his team-mate on the edge of the area.
Thomas was key again to the second, his lofted pass out wide allowing Lucas Hernandez to volley first-time into the six-yard box, where Nikola Kalinic should have finished. His effort was parried out and Saul slid in the rebound.
Getafe's frustration built and boiled over at the end as Dakonam was shown a second yellow card in the 88th minute for a rash challenge on Thomas Lemar and then Cabrera followed him three minutes later for applauding the referee. It was a feisty end to a comfortable Atletico win.
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