Four out of four for free-scoring Spurs
First half strikes from midfielders Tom Huddlestone and Jamie O'Hara and a first goal for England forward Peter Crouch put Spurs 3-0 ahead at half-time.
The 2008 League Cup winners and losing finalists last season added two more after the break through David Bentley and Russian international Roman Pavlyuchenko after Rovers had pulled one back from the penalty spot.
Wigan Athletic, beaten 5-0 by Manchester United last Saturday, endured a miserable evening at second division Blackpool losing 4-1 and becoming the first Premier League team to exit the competition.
Premier League Stoke City edged past third division Leyton Orient 1-0 thanks to striker Dave Kitson's extra-time goal, while second division West Bromwich Albion beat fourth division Rotherham United 4-3 in extra time with Simon Cox grabbing the winner.
Elsewhere, there were wins for Carlisle United, Cardiff City and Newcastle United.
The third round draw, which takes place on Saturday, introduces the Premier League sides involved in European competitions this season.