Valencia fell to a damaging 2-1 defeat at Almeria which leaves them in the relegation zone, while nine-man Real Betis lost 2-0 at home against Cadiz, denting their bid for Champions League football.
Defenders Nahuel Molina and Mario Hermoso struck first-half goals two minutes apart to put Atletico into a dominant position at Vallecas.
Rayo had defender Florian Lejuene sent off in the second half for a professional foul on Alvaro Morata, allowing Atletico to stroll, but Fran Garcia's powerful drive gave the hosts some hope in the final stages.
Atletico held on to keep up the pressure on their rivals, champions Real Madrid, who lost 3-2 at home against Villarreal on Saturday.
Diego Simeone's side took the lead after a slick break, with Yannick Carrasco and Antoine Griezmann combining well, before the latter played a fine pass to Alvaro Morata.
The striker nudged the ball on to Molina, racing up on the right, who swept the ball home to net his first goal for the club.
Molina dedicated his strike to team-mate Angel Correa, absent from the squad after his mother died this week, raising the Argentine's number 10 shirt into the air.
Atletico soon grabbed their second with Hermoso heading home from Carrasco's corner for his fourth goal of the season.
After Lejeune was dismissed Atletico cruised, with Griezmann, Morata and Marcos Llorente all missing chances.
However Garcia smashed past Jan Oblak from distance in the 85th minute to give Atletico a scare, but they saw the game out to move six points ahead of Real Sociedad in fourth and put Real Madrid firmly within
- Betis beaten -
Nine-man Real Betis fell to a shock 2-0 home defeat by Cadiz, leaving Manuel Pellegrini's side sixth in La Liga.
After Villarreal's win on Saturday they leapfrogged Betis, who could not go back ahead of Quique Setien's side as they stumbled in an Andalucian derby.
Betis playmaker Sergio Canales made his comeback after being given a reprieve from a four-game ban by court order, but it only lasted 38 minutes.
The Spaniard was sent off for pulling down Ruben Sobrino and stopping the Cadiz forward from running through on goal.
Cadiz took the lead from the penalty spot early in the second half through Ruben Alcaraz after Juan Miranda handled a free-kick.
The visitors netted their second before the hour mark when Theo Bongonda broke away and unselfishly teed up Chris Ramos to tap home his first goal for the club.
Betis were soon reduced to nine men on a miserable afternoon for the hosts as Aitor Ruibal twice swung his elbow at Fali and was dismissed.
"I'm sorry team, fans, Real Betis," wrote Canales on Twitter.
"Today I made a mistake, a grave error, and I'm responsible for the defeat.
"I have to be self-critical and keep working like never before to help you."
Vedat Muriqi hit a brace, including a stoppage-time penalty, to rescue Real Mallorca a 3-3 draw at Real Valladolid.
On Monday leaders Barcelona can move 15 points clear with a win against Girona.