A thoroughly deserved 2-1 win at home to second-placed Atletico Madrid last weekend prompted talk of a realistic chance of a place in Europe next term and enhanced Rayo's reputation as one of Spain's "giant-killers".
The modest club, who are in administration and whose 15,000-seater stadium has only three stands with one end used for advertising, are transformed from the side that were mired in the third-tier in Spanish football between 2004 and 2008.
They narrowly avoided relegation last season after coming up from the second division but under the guidance of coach Paco Jemez and fired by the goals of captain Piti and fellow forward Leo Baptistao, they have become a genuine force, with wins at Valencia, Athletic Bilbao and Malaga.
"We are now in a situation where we only have to look forward," Jemez told a news conference this week.
"We are not going to be satisfied with what we have done and we want to continue making history," the 42-year-old added. "We have to enjoy everything we are doing."
They face a monumental task at champions Real, who are undefeated at the Bernabeu in all competitions this season but have suffered erratic form away from home and are four points behind Atletico and 16 behind leaders Barcelona.
Jemez said Rayo would not be changing their free-flowing playing style, which has drawn comparisons with Barca, and would be going out to enjoy themselves on Sunday.
"We don't need to be scared in any way, we just have to show what we have been showing up to now," he said.
"We are going to go there without any kind of complex with a lot of desire to enjoy ourselves and play a good match."
Barca have had a restful week with their Champions League last 16 first leg at Serie A side AC Milan not until next Wednesday and can go 15 points clear of Atletico with a win at 14th-placed Granada on Saturday.
Forward David Villa is unavailable after failing to recover from kidney stones, the club said on Thursday.
Atletico have won all 12 of their home matches this term but were beaten in their last two away fixtures and play at mid-table Real Valladolid on Sunday.
