Whatever Harry Redknapp received for Christmas, nothing will come close to the "present" the Tottenham Hotspur chairman, Daniel Levy, gave him at 4pm on deadline day in August. Rafael van der Vaart was the gift and the Tottenham manager has been reaping the benefits ever since. Back from a month on the sidelines, the Dutchman scored both goals against Aston Villa, just as he did at White Hart Lane in October when Spurs triumphed by the same scoreline.

It was another outstanding contribution from Van der Vaart on a night when Tottenham were forced to play with 10 men for 63 minutes after Jermain Defoe was sent off for striking James Collins in the face during an aerial challenge.Tottenham of old might have crumbled in those circumstances but Redknapp's side demonstrated strength in the face of adversity against Internazionale earlier this season and the man at the centre of that remarkable second-half performance in Milan was at it again here.

With Villa pressing for an equaliser after the interval, Gareth Bale went on one of those mesmerising runs that almost inevitably end up with defenders sitting on their backsides and Spurs supporters up on their feet. Villa's defence braced themselves for Bale to shoot after a 60-yard dash but the Welshman instead had the presence of mind to pick out Aaron Lennon, whose own unselfish pass was expertly tucked beyond Brad Friedel by the ruthless Van der Vaart for a wonderful team goal.

It was Van der Vaart's 10th in 15 appearances and gave Spurs the breathing space they needed at a time when Villa had been cranking up the pressure. The lively Marc Albrighton, who is just about the one shining light in this increasingly bleak season for Villa, ensured that Redknapp had to endure a nervous final eight minutes when his inswinging cross drifted beyond Heurelho Gomes, but Tottenham refused to buckle and held on for a deserved three points.

The only downside for Redknapp was the dismissal of Defoe, who faces an automatic three-match suspension, with Spurs unlikely to appeal against the sending off. The England international complained bitterly when Martin Atkinson brandished a straight red card but it was difficult to argue with the referee's interpretation of the incident. Defoe led with an arm and made contact with the side of the Villa captain's head as he challenged for a high ball midway inside the Villa half.

"I haven't seen a replay. The boys [the backroom staff] all looked at it at half-time and they thought it was harsh – they said he didn't take his eye off the ball," said Redknapp, who laughed off a touchline spat with Villa's Robert Pires. "Losing Defoe made it difficult but I said to the players at half-time that we could get another one on the break because of the pace we have got with Aaron and Gareth. And it was a fantastic second goal. Really top-class."

Defoe's dismissal was not the only big decision Atkinson made on a night when both managers. Redknapp felt Tottenham had a legitimate goal chalked off in the 16th minute, when Younes Kaboul's effort was ruled out after Alan Hutton was adjudged to have retrieved the ball from beyond the byline. At the other end, Gérard Houllier claimed Villa should have had a penalty in the ninth minute, when Gomes left Emile Heskey nursing a twisted ankle after colliding with the forward.

Spurs took the lead not long after that incident, when Luka Modric delivered a sublime pass that exposed Stephen Warnock's poor positioning and invited Hutton to run clear on the right flank. The full-back skidded a low centre that eluded Collins but ran perfectly into the path of the onrushing Van der Vaart who side-footed home without breaking his stride for the first of his two goals. "He's been fantastic," Redknapp said of the £8m signing from Real Madrid. "He's a 15-to-20-goal-a-season man."

How Villa could do with one of those. These are worrying times for a club who were going head-to-head with Spurs last season but are now travelling in the opposite direction.

The sight of the midfielders Fabian Delph and Stilian Petrov returning from injury provided Houllier with "a few positives", although it is doubtful if the home supporters took any comfort from a result that leaves them facing a relegation battle. With a trip to Manchester City on Wednesday and Chelsea away on New Year's Day, there is unlikely to be much festive cheer at Villa.