Atletico had lost their past two league games, including a derby defeat at home to Real Madrid last weekend, and they gave another below-par performance at Vallecas on Saturday.
Rayo, who remain in LaLiga's relegation zone after a third straight loss, had the better chances with Adrian Embarba and Raul de Tomas calling Atletico goalkeeper Jan Oblak into action.
But Atletico marked Simeone's new contract with three points after Griezmann's 74th-minute volley deflected in to give the striker his eighth goal in his past six appearances against Rayo.
8 - Atletico de Madrid’s Antoine Griezmann has scored in each of his last six appearances against Rayo Vallecano in all competitions (eight goals). Key. pic.twitter.com/EfOiegB1uP— OptaJose (@OptaJose) February 16, 2019
Saul Niguez headed off target from Griezmann's early cross but the first big chance fell to Rayo with Embarba unable to beat Jan Oblak after being sent by De Tomas.
Atleti were indebted to Oblak for an even better save in the 34th minute, the goalkeeper twisting to deny Embarba after another incisive De Tomas pass.
Simeone sent on former Rayo loan star Diego Costa for his first appearance since the start of December as Atletico fielded the fit-again striker with Griezmann, Alvaro Morata and Thomas Lemar across the front.
But Rayo continued to threaten with Oblak quick off his line to deny De Tomas after he ran on to a sensational long ball from Alejandro Galvez.
De Tomas had a weak penalty appeal turned down after a challenge from Jose Gimenez and Atletico finally broke the deadlock in the 74th minute.
Morata won the ball in the box and Griezmann pounced on the loose ball with goalkeeper Stole Dimitrievski beaten by a decisive deflection on the match-winning strike.
Rayo had one big chance to claim a deserved point in added time but Oblak held on to Abdoulaye Ba's header.
What does it mean? Simeone's side back on track
Simeone was at risk of losing three consecutive league games for the first time in seven years in charge, which would have been an inauspicious way to celebrate signing a new contract.
Griezmann comes up trumps yet again
Atletico struggled to create against a disciplined Rayo side but they only needed a half-chance to score the winner. Griezmann's improvised finish hit Jordi Amat on its way in, but he clearly relishes playing Rayo as he has scored in this fixture six times in a row.
Morata drought continues
Costa's return to Atletico's squad could have been the kick Morata needed to jumpstart the boyhood Rojiblancos fan's career at the club. Morata struggled to make an impact and wasted an early headed chance by nodding Griezmann's cross at Dimitrievski, although he was involved in the winner.
Key Opta Facts:
- Griezmann's goals have been worth 13 points for Atletico in LaLiga this season, the most by a player for a team in the competition.
- He has scored the first goal of LaLiga games seven times, more than any other player this season.
- Griezmann has scored nine goals versus Rayo in all competitions, more than against any other opponent in his career.
- The France star has been involved in 10 of the last 13 Atletico goals in LaLiga (eight goals, two assists)
- Rayo have only won one of their last 15 games against Atletico in LaLiga (D3 L11), 2-1 at Vallecas in February 2013.
Juventus visit the Spanish capital for the first leg of their last-16 Champions League clash on Wednesday with Atleti at home to Villarreal in the league four days later. Rayo are at Getafe on Saturday.