It was an ugly spectacle but relegation-threatened Rangers will celebrate a point against the club that fired Redknapp last June and appointed Villas-Boas as his successor.
The build-up to Saturday's London derby saw Redknapp play down the existence of animosity with Villas-Boas and the rivals embraced after emerging from the tunnel for kickoff.
While it was not quite the complete revenge QPR's manager may have privately sought, the draw meant his side have taken four points from their last two matches against top four opposition following their 1-0 victory over Chelsea on Jan. 2.
When asked if current form could mean QPR would not spend in the January transfer window, Redknapp said: "I think if you think that is going to happen we would have a rude awakening at the end of the year. We need to strengthen the squad, we are short in certain areas. When there are games you have to open up and try and win we have to try and improve for sure."
He also said QPR is close to loan deal for Spurs midfielder Jake Livermore.
Well organized and tenacious, for long spells QPR frustrated Tottenham, who had won nine of their past 11 games before Saturday and scored an average of three goals in each of their past four matches.
"It is difficult to break them down and only if you score is it possible to find more spaces," Villas-Boas said.
The reflexes of keeper Julio Cesar kept Rangers in the hunt, especially early on when Jermain Defoe and Emmanuel Adebayor probed for the opener, but their safety-first approach meant Hugo Lloris was untroubled.
Lone striker Adel Taarabt cut a frustrated figure at times, frequently isolated by his team's refusal to attack with numbers, but Rangers still had occasional opportunities on the break to snatch victory.
Villas-Boas was hoping Tottenham would be in a position to take advantage of any ground lost by their rivals in Sunday's matches at Old Trafford and the Emirates Stadium, but QPR proved uncompromising opposition.
Referee Lee Probert engaged in an early discussion with Cesar after Sandro had shot wide of the right post before the match burst into life in the fifth minute.
Defoe's fierce attempt from the edge of the area was brilliantly pushed onto the left post by Cesar and a heartbeat later the Brazilian dived to deny Adebayor, who should have done better with the goal at his mercy.
The ensuing corner saw Cesar keep out Bale at the near post and moments later Lennon tumbled as he dashed into the box, but Probert was unconvinced.
Dawson, who turned down a move to QPR in the summer, came to the rescue again with an inch-perfect tackle on Stephane Mbia on the edge of the area when he was the final defender in front of Hugo Lloris.
Sandro departed the field having gone down clutching his right knee as he reached for the ball, so Scott Parker came on to anchor the midfield.
QPR was well drilled and solid with its 4-5-1 formation frustrating Spurs, though panic crept into the home side in the 35th minute when Shaun Derry gave the ball away to Bale only for the Wales winger to send his cross into the stands.
The chances had dried up for Tottenham with Parker's decision to pull the trigger from 40 yards evidence of their lack of opportunity.
Wright-Phillips showed dazzling footwork to launch a run to the edge of the area that ended when a disappointing shot drifted wide of the left post.
Parker blasted just over the crossbar and Bale and Kyle Walker went close with free-kicks as Tottenham made a promising start to the second half that continued when Defoe was kept out by Cesar.
It took 20 minutes for QPR to break Spurs' stranglehold of the second half with Taarabt showing skill and tenacity to reach the byline only to then retreat down a dead end.
Taarabt threaded a beautiful pass to Fabio da Silva but there was no one to pick up the Brazilian's lethal square pass because of Rangers' lack of numbers in attack.
Spurs still controlled possession but QPR was looking dangerous on the break, although Mbia's late theatrics when he collided with Lloris and began rolling on the floor were risible.