London: Tottenham once again looked uncomfortable in their new abode as second-tier Barnsley held out for 65 minutes before succumbing to a 1-0 defeat in a front of a sparse 23,926 crowd.
England midfielder Alli finally broke the deadlock with a smart finish from Kieran Trippier's cross to give Tottenham win number two at Wembley following last week's Champions League success against Borussia Dortmund.
Elsewhere in the third round, Premier League side Stoke slumped to a surprise 2-0 defeat at second-tier Bristol City.
Famara Diedhiou headed City in front in the 50th minute and Matt Taylor added the second on the hour.
Burnley also bowed out after losing 5-3 on penalties following a 2-2 draw with second-tier Leeds at Turf Moor.
Roy Hodgson got his first win as Crystal Palace manager as Bakary Sako sealed a 1-0 win against Huddersfield.
The former England coach's first game had ended in a 1-0 home defeat against Southampton in the Premier League at the weekend.
But Sako nabbed the first goal of the Hodgson era with a close-range header from a 13th-minute corner at Selhurst Park.
It was Palace's first goal since August 22 and Mali forward Sako's first since August 2015.
West Ham beat Bolton 3-0 with goals from Angelo Ogbonna, Diafra Sakho and Arthur Masuaku.
Alfie Mawson and Jordan Ayew scored in Swansea's 2-0 win at Reading.
Bournemouth beat Brighton 1-0 just four days after defeating their south-coast rivals in the Premier League.