The Uruguay international struck on the stroke of half-time at the Wanda Metropolitano to pull Atletico level with the visitors, who went ahead through a Santi Mina goal just 13 minutes into the match.
The 34-year-old struck again early in the second half to give the home team the lead and put them on course to extend their lead at the top of LaLiga.
Suarez breaks LaLiga record
16 - Luis Suárez 🇺🇾 has scored 16 goals in his first 17 games for Atlético de Madrid in LaLiga, becoming the fastest player to reach 16 goals for the same club in the competition in the 21st century (Cristiano Ronaldo 🇵🇹 - 15 goals for Real Madrid in 2009/10). Amazing. pic.twitter.com/wHbLRFdA7P— OptaJose (@OptaJose) February 8, 2021
A win for Atleti on Monday would put the capital club 10 points ahead of Barcelona and Real Madrid at the top of the table, though Simeone's team still have a game in hand.
Suarez has been pivotal in their impressive season so far. He leads the league goal chart, having scored three more than Barca sensation Lionel Messi.
Barcelona's Suarez mistake
The Camp Nou side's decision to let Suarez leave to join their domestic rivals has been ridiculed as a mistake by many, with his former team-mate Iago Aspas adding his voice to the list of critics last week.
Atletico boss Simeone said last month that he knew the attacker would make a big impact in the Spanish capital after his first phone call with him before the move went through.
Suarez even more important amid Covid-19 outbreak
The Spanish side have seen several players ruled out of their upcoming matches with Covid-19.
Thomas Lemar and Hector Herrera are the latest to test positive, with Joao Felix, Moussa Dembele, Yannick Carrasco and Mario Hermoso already in isolation.
Those six will not be able to feature against Thomas Tuchel's side unless they return negative tests before the match, which could be moved to a neutral venue because of travel restrictions in Spain.