It will take more than an unforgiving fixture schedule to stop Tottenham Hotspur in their tracks. André Villas-Boas was unhappy with being asked to play three games in six days but a third straight victory across that period ensured that the Spurs manager departed Villa Park with a smile on his face. Spurs have now won eight of their nine matches this season, scored 22 goals in the process and conceded one. Confidence is sky high.

This impressive performance provided tangible evidence of the strength in depth in a Tottenham squad rebuilt in the wake of Gareth Bale's departure. Jermain Defoe has yet to start in the Premier League this season but he scored his fifth and sixth cup goals of the campaign to start and complete Tottenham's rout – a repeat of their 4-0 win here on Boxing Day. In between Defoe's goals, Paulinho grabbed his second in three days and Nacer Chadli, a second-half substitute, opened his Spurs account. Lewis Holtby also caught the eye with a fine display that included three assists.

A miserable night for Aston Villa got worse when Paul Lambert revealed that Christian Benteke, who limped off against Norwich City on Saturday with a hip flexor problem, would be out for up to six weeks. Villa's most influential player has scored four of their six league goals this season and his absence leaves a huge void. "It's not as bad as we feared it was going to be," the Villa manager said. "Maybe four, five or six weeks, we'll just have to see. It's a muscle injury. Thankfully it's not too serious. It has got a lot better, he is also feeling a lot better and the international break certainly helps us."

Although a weakened Spurs team were much too strong for a depleted Villa side, the complexion of the game may well have changed had the referee, Jonathan Moss, penalised Jan Vertonghen for a clear foul on Nicklas Helenius in the penalty area at the start of the second half. Struggling to keep his footing, Vertonghen tugged at Helenius's shorts, pulling them down to leave the Dane shooting for goal sporting a pair of white briefs.

It was a comical moment, although Lambert, quite understandably, failed to see the funny side. "It's the first time I've seen something like that happen. I don't think anybody could believe it wasn't pulled back [for a penalty]," he said. "We were still in the game at 1-0, I thought it was a big moment."

Helenius was probably guilty of being too honest and trying to stay on his feet when plenty of other players would have gone to ground, although that was still no excuse for Moss failing to point to the spot. "I can understand that Paul won't be happy with the decision," Villas-Boas said. "Most likely in this situation there isn't an advantage to be played and the penalty has to be whistled. It was a difficult decision for Jon and probably we got away with it."

That was a rare moment of consternation for a Spurs side in which Kyle Walker, Vertonghen and Paulinho were the only survivors from the XI that started against Cardiff on Sunday. Defoe got Spurs on their way at the end of the first half with a glancing header from Holtby's sublime pitching wedge of a pass. Paulinho then doubled Tottenham's lead with a close-range volley from Holtby's corner three minutes after Vertonghen had undressed Helenius.

Defoe turned creator in the 87th minute, when his pass invited Chadli to run clear in the inside-left channel before beating Jed Steer at his near post, and the England international made it 4-0 in the closing seconds after running on to Holtby's pass and rounding Steer in the Villa goal.

"I think the team is playing very well, we have great strength in our squad," said Villas-Boas, who praised Defoe for his contribution. "He is doing extremely well, ticking all the right boxes. It was once again a great performance – two goals, one assist, available for the team, great spirit. I think you have to give him credit for what he has done here."