Rubin looked dead and buried when they were 1-0 down and had Alexander Prudnikov sent off for two bookable offences in as many minutes.
But the Russian outfit clawed back to earn a 1-1 draw at the Estadio Benito Villamarin through a Roman Eremenko penalty.
Head coach Vladimir Maminov will be satisfied to take an all-important away goal into the return leg at the Kazan Arena in a week's time.
It promises to be a feisty affair after this tie saw nine yellow cards and one red.
Betis dominated for the majority of the game and took less than four minutes to take the lead when Didac Vila's effort across goal beat Sergey Ryzhikov with the first shot of the game.
The home side sensed they could kill the tie and an 18-yard shot from Leo Baptistao nearly did so, but Ryzhikov parried the ball away.
The Betis onslaught continued and Rubin were fortunate to only be a goal down at half-time.
Shots were few and far between for Rubin but Sergey Kisliak made sure goalkeeper Antonio Adan knew the away side were not out of the contest.
At 1-0 down, there was always a chance for the away side to nick a goal.
It was 15 minutes from time when Betis' Lorenzo Reyes brought down Gokdeniz Karadeniz in the area and referee Serge Gumienny pointed to the spot.
Eremenko did not pass up the opportunity and slotted the ball in to the left-hand corner to make it 1-1.
Rubin withstood a late surge from the home side who knew they should have put the game out of reach by half-time.
A final desperate shot by Didac from 25 yards out sailed over the bar and Rubin were happy to play out the final five minutes of stoppage time.