A sensational first-half free-kick from Roman Pavlyuchenko put Tottenham top of Europa League Group A.
A much-changed Spurs side found it hard to settle against Rubin, who consistently threatened on the break.
However Russian Pavlyuchenko stunned his compatriots with an unstoppable 25-yard drive into the top corner.
Spurs goalkeeper Heurelho Gomes, making only his third start of the season, made a string of fine saves to earn his side an important victory.
With only two fit centre-backs available, Tottenham boss Harry Redknapp employed young midfielder Jake Livermore at the back alongside Sebastien Bassong but Spurs struggled against a seasoned Champions League outfit, who beat Barcelona at the Nou Camp in 2009-10 and continually worked their way between the home defence to create some golden opportunities.
Roman Sharonov rose unchallenged to head a corner wide, while diminutive winger Gokdeniz Karadeniz ghosted in with a diving header from the edge of the six-yard box that was acrobatically kept out by Gomes.
As expected, Livermore was comfortable in possession and he grew into his defensive role, but positional inexperience allowed Nelson Valdez to drift free and he should have tested Gomes more seriously with his close-range flick.
The lead up to the winning set-piece was curious as Portuguese referee Manuel De Sousa moved the ball back from two yards inside the D, where the foul on Danny Rose was clearly committed, to the outer edge.
However, it allowed Pavlyuchenko more space to keep the ball down after clearing the wall and his magnificent strike could not have been better placed as it arrowed into the very top corner of the goal.
In a further twist, Rubin were insistent that Kyle Walker, who crouched behind the wall in front of the goalkeeper but dashed out of his eyeline before the ball was struck, should have been flagged offside.
After the break Gomes, relegated to third choice at White Hart Lane this term, smartly kept out a well-struck long range effort from Aleksandr Ryazantsev as the visitors continued to threaten.
The athletic Walker, one of Tottenham's more effective attacking elements with his raids from right-back, made a timely intervention after Rose had been dispossessed and even Aaron Lennon was needed to provide an interception in the danger zone to foil another attempt by the Russians.
Spurs often struggled to retain possession and find their customary fluency, but a fine ball from cultured central midfielder Tom Carroll freed Lennon in his more familiar role on the flank and he jinked past his man before sending a looping cross that Jermain Defoe headed goalwards, only for goalkeeper Sergei Ryzhikov to scramble clear.
Redknapp was determined to secure victory and sent on Younes Kaboul and star playmaker Luka Modric to shore things up.
The decision was fully justified when Kaboul's superb diving challenge thwarted substitute Obefami Martens, the former Newcastle and Birmingham striker, who was poised to shoot.
Tottenham manager Harry Redknapp:
"We wanted to get the points tonight and really I can look to send the kids over there to play." [in the return match in Russia on 3 November]
"It's a horrendous journey before you play on the Sunday. It's not what you want. It will be a good experience for some of the young players to go and I can save the senior ones for the game on the Sunday.
"I thought it was a good performance. We had to hang on a little at the end but I was pleased with us.
"When Pav lined it up I had a feeling he was going to score because he is a very clean striker of the football. I was pleased for Gomes. He was great tonight. I would like to think he still has a big future here."