After taking a 1-0 lead into half-time courtesy of a Mario Suarez goal in the 29th minute, Atletico appeared to put the result beyond doubt following a devastating three-goal blitz early in the second half.
 
Koke, Arda Turan and Falcao - from the penalty spot - all got their names on the scoresheet within the space of seven minutes to put Atletico up 4-0 after just 56 minutes and leave Rayo heads spinning.
 
Atletico held on to their four-goal buffer right up until the 81st minute and appeared destined for a comfortable victory but a quick-fire brace from Andrija Delibasic and a follow-up from Leo with just one minute of regular time remaining saw Rayo roar back into life and set up a grandstand finish.
 
However, the hosts managed to hang on for a memorable 4-3 win and move up to fifth on the La Liga table.
 
Third-placed Mallorca blew a chance to move to second place after being held to a 1-1 draw by bottom-placed Osasuna at Estadio El Sadar.
 
The result could have been even more embarrassing for the visitors after Osasuna opened the scoring in the 69th minute thanks to a Kike Sola header.
 
But Mallorca saved their blushes to a degree nine minutes later when Tomer Hemed produced a header of his own to level scores and ensure the sides shared the spoils.
 
Granada were another bottom-three side to score an upset draw against more-fancied opposition when they held Deportivo La Coruna to a 1-1 result.
 
Deportivo grabbed the lead four minutes before half-time through Nelson Oliveira but Floro Flores ensured the hosts wouldn't finish the match empty-handed when he goaled in the 81st minute.
 
In other results, Real Sociedad defeated Real Zaragoza 2-0 while Espanyol and Athletic Bilbao played out an entertaining 3-3 draw.