Without the injured Cristiano Ronaldo, Real’s title hopes looked in tatters when early goals from Adrian Embarba and Miku put Rayo 2-0 in front.
However, Bale’s powerful header halved the deficit before half-time and he fired home the winner nine minutes from time after Lucas Vazquez had equalised early in the second period.
The visitors got off to a terrible start as they struggled to deal with the difficult conditions caused by a torrential downpour in the Spanish capital.
Embarba tapped home the opener from close range after Bebe’s determined run and cross had opened up the Madrid defence with just seven minutes gone.
It was 2-0 inside 15 minutes as shocking Real defending from a corner allow Miku to sweep home his eighth goal of the season.
Madrid have now won the last 16 meetings between the sides stretching back 16 years, but Rayo could have been out of sight but for a fine flying save from Keylor Navas to prevent Bebe’s long-range effort finding the top corner.
In the absence of Ronaldo, Bale took responsibility to drag Madrid back into the game as he rose highest to power home Toni Kroos’s corner 10 minutes before half-time.
Madrid suffered another blow before the break, though, as Karim Benzema limped off with a knee injury making him a serious doubt to travel to Manchester in midweek.
Vazquez replaced the Frenchman and it was the diminutive winger who brought Real level in unusual fashion as he powered home a header from Danilo’s cross six minutes into the second half.
Rayo struggled to contain the wave upon wave of Madrid attacks that ensued as Vazquez just failed to connect with Bale’s cross before Jese Rodriguez fired straight at Juan Carlos with just the goalkeeper to beat.
However, it was fitting that Bale was the man to decide the game as he pounced on a loose pass midway inside the Rayo half and surged forward before striking low and hard past Juan Carlos for his 18th goal of the season.
Rayo had the chance to snatch a point in stoppage time, but Miku’s shot was deflected over as Madrid registered their ninth consecutive La Liga win.
