Aston Villa 3 Rotherham 0 - match analysis and pictures

But with their Bradford beating still raw, they began to heal the wounds by cruising past Rotherham.

Paul Lambert revealed that the semi-final exit to the Bantams last season was his lowest ebb as Villa boss, the two-legged defeat the nadir of a difficult year.

This time, though, Villa negotiated their early banana skin with comfort to net a home third round tie with Tottenham after riding an early Rotherham assault.

The teams contested the first ever League Cup final in 1961 – with Villa winning 3-2 on aggregate after Rotherham had won the first leg 2-0.

Fixture congestion meant the second game at Villa Park wasn't played until the start of the 1961/62 season – just eight days before the claret and blues started their defence.

There was little need for any rousing comeback this time, however, as final goalscorers Alan O'Neill, Peter McParland and Harry Burrows watched the class of 2013-14 ease past the Millers. Andi Weimann and Christian Benteke underlined their class with clinical first-half strikes and Fabian Delph grabbed the goal his performance deserved.

The Chuckle Brothers are honorary presidents of the Millers, but there were no cheap laughs for the visitors as Villa did a professional job.

Lambert's strong selection underlined the importance of the competition and the fact that Villa do not play again until Newcastle visit on September 14.

With a silverware drought stretching back to 1996 – the 3-0 League Cup win over Leeds – the competition offers real chance of success to the claret and blue.

Since they last won it Leicester, Blackburn, Middlesbrough, Swansea – and Birmingham – have all punctured the traditional dominance of the "big four".

The luck of the draw deserted Villa when they were handed a clash with big-spending Spurs next time round.

But they are at home and within Lambert's regeneration plan will be space for Wembley success – and the Capital One Cup should be on the priority list. And one target has been knocked off now after the first clean sheet in a competitive outing for 31 games.

While the nature of the opposition must be taken into account the shutout will, regardless, breathe confidence into a previously unsteady defence.

Jed Steer was the man to keep it – on debut – as he, Joe Bennett and Karim El Ahmadi came in for Brad Guzan, Matt Lowton and Antonio Luna.

Rotherham started brightly as Alex Revell glanced well wide before Lee Frecklington's cross eluded him in the middle. Benteke fired over with the visitors' enterprise impressing, but they were masters of their own downfall on 19 minutes when Kari Arnason gifted Weimann the ball.

The Austrian raced down the right and – when his attempted pass ricocheted back off the covering Arnason – blasted his shot into the top corner from 20 yards.

It eased the nerves and Villa began to squeeze the life out of their League One opponents who started to wilt. And they handed Villa a second goal five minutes before the break.

Again Arnason surrendered possession, this time to Ashley Westwood, who fed Gabby Agbonlahor and he skipped down the right to cross for Benteke to crash in a far-post header.

Martin Pringle shot just wide in response, but the game was over on 53 minutes when Delph capped another lively outing by volleying in after a neat one-two with Benteke.

Scott Shearer then saved Joe Bennett's header as Villa turned the screw.

Michael O'Connor fired a free-kick over, but the hosts were content to see the game out.

The road to Wembley starts again and Villa will hope to avoid another dead end.

Villa (4-3-3): Steer 7; Bacuna 7, Vlaar 7, Okore 7, Bennett 6; El Ahmadi 7, Westwood 7, Delph 8 (Sylla, 60 6); Agbonlahor 7 (Tonev, 67 6), Benteke 7 (Helenius, 67 6), Weimann 7. Subs not used: Clark, Herd, Lowton Guzan (gk). Booked: Delph.

Rotherham (4-5-1): Shearer; Skarz, Arnason, Morgan, Bradley; Pringle (Brindley, 84), O'Connor, Milsom (Tidser, 58), Frecklington, Agard (Tubbs, 84); Revell. Subs not used: Hylton, Rowe, Collin (gk).

Referee: Simon Hooper (Wiltshire). Attendance: 22,447.