Adebayor's double on his home debut helped earn Spurs a morale-boosting first home win of the season.
Luka Modric opened the scoring with a blistering 20-yard strike before Charlie Adam picked up a second yellow card for a late foul on Scott Parker.
Martin Skrtel, who had a torrid afternoon at right-back thanks to Gareth Bale, was sent off for two bookings in the second half before Jermain Defoe calmly slotted home to make it 2-0 in the 66th minute.
Adebayor, who scored on his debut against Wolves last week, scored a tap-in soon after before he volleyed past Jose Reina to seal the win in stoppage time.
Fresh off the back of last week's first win of the season, Tottenham looked a class apart against their Champions League rivals, but their cause was helped by the two dismissals.
Reds boss Kenny Dalglish, who met referees' chief Mike Riley this week after venting his anger at Mark Clattenburg's decisions against his team last weekend, was furious with Mike Jones' decision-making at times on Sunday, stopping the official as he went down the tunnel at half-time.
Right from the kick-off, it looked like there was only ever going to be one winner in this match.
After his team's midweek trip to Greece, Harry Redknapp reverted to the same XI that beat Wolves and they stamped their dominance on the game from the whistle.
Adebayor brushed past his marker to gain a yard in the box but miscued his volleyed wide from 10 yards.
Daniel Agger then blocked Defoe's goal-bound shot before Modric brought White Hart Lane to its feet with his blistering opener after six minutes.
The Croatian, who had been the subject of at least three bids from Chelsea this summer, picked up a loose ball 20 yards out and hammered his strike into the top left-hand corner of Reina's goal.
Referee Jones handed out his first booking of the afternoon to Adam for a foul on the goal scorer.
Liverpool were struggling to get in to the game and at times, their passing was poor.
They thought they had equalised though when Luis Suarez tapped home after but the linesman ruled the Uruguayan was offside when he picked up the ball from Andy Carroll.
Agger then hobbled off after slipping and injuring his chest. He was replaced by debutant Sebastian Coates.
Liverpool's afternoon went from bad to worse just before the half hour when Adam caught Parker in the leg with his studs up as the England midfielder went for a volley.
Jones reached for his pocket and issued the second yellow which reduced the visitors to 10 men.
Skrtel, clearly struggling to keep up with Bale's electric pace, saw yellow for a cynical bodycheck on the Welshman.
Like Bale, Adebayor was proving to be a real handful. The striker brushed off Coates and ran towards goal but the defender hacked him down from behind and earned a booking.
Younes Kaboul and Defoe both came close to making it 2-0 before the break as Spurs' dominance continued.
Suarez was annoyed he did not get a foul on the stroke of half-time after a tussle with Benoit Assou-Ekotto and his protest at the referee earned him a booking.
Reds boss Dalglish, who last week criticised Clattenburg for not giving his side a penalty at Stoke, was furious with Jones and remonstrated with the official as he went down the tunnel at half-time.
Spurs almost scored a minute into the second half when Kyle Walker crossed for Adebayor, who played in the unmarked Defoe his poor shot dribbled wide from six yards.
Liverpool were convinced they should have had a penalty when Carroll thought his jump in the box was impeded by Assou-Ekotto but Jones waved play on.
Liverpool's miserable afternoon continued in the 63rd minute when Skrtel clipped Bale's heels as he turned to run down the flank.
The former Southampton man punched the turf in apparent pain and Jones sent the Liverpool defender off with a second booking.
Two minutes later it was 2-0. Substitute Rafael van der Vaart sent Defoe racing through the middle, and after holding off Jose Enrique's challenge, the England striker spun and shot low past Reina..
Just two minutes passed before Adebayor scored Tottenham's third.
Reina spilled Defoe's shot and the former Gunners man reacted quickly, lifting the ball over the scrambling Spaniard before tapping in to an empty net.
Liverpool could not get a touch of the ball as Spurs made their numerical advantage count.
With the game well won, Tottenham eased their foot off the accelerator.
Van der Vaart tried a cheeky chip at the other end in injury time but Reina was equal to his effort.
Adebayor then made it 4-0 in the final seconds when he picked up Assou-Ekotto's cross to control and calmly volley past Reina.