In the week their manager Harry Redknapp learned he would not succeed Fabio Capello as England manager, Spurs played more like the side they were before the speculation he would become national boss began.
Bolton's Nigel Reo-Coker cancelled out a stunning strike from Luka Modric at the Reebok Stadium but three goals in nine minutes from Spurs, one from Rafael van der Vaart and Adebayor's double, ended the contest.
The victory took them within a point of third-placed Arsenal but left Bolton in deep relegation trouble.
It was an emotional night for the hosts with Fabrice Muamba returning to the ground for the first time since suffering a cardiac arrest during the FA Cup tie between the same two teams in March.
The Trotters midfielder accepted a standing ovation from all sides of the ground as he was introduced on the pitch before kick-off but attention then shifted to Bolton's battle against the drop.
The hosts' failure to make the most of a dominant spell after Reo-Coker's equaliser proved costly as they slipped to a defeat that leaves them in the bottom three.
They showed determination and composure early on in what was their game in hand but it was Spurs who had the first serious opportunities when Adam Bogdan was forced into a double save.
Bogdan, outstanding in the rearranged cup game against Spurs, parried a long-range drive from Gareth Bale and then reacted quickly to deny Van der Vaart.
Bale made a cutting charge into the area and pulled the ball back from the byline but there was no-one on hand to turn in.
Bolton pieced together a nice move to release Dedryck Boyata in the box but the right-back could only pick out Brad Friedel while David Ngog was unmarked in front of goal.
Bolton made another swift counter-attack as Martin Petrov broke clear down the left and whipped in a low cross which just evaded Kevin Davies.
Chris Eagles picked up possession and found Ngog but the Frenchman's shot was smothered by Friedel.
Spurs took the lead with Modric's spectacular strike after 37 minutes.
The visitors won a corner after Bogdan saved from Van der Vaart and the ball was put behind despite suspicion of handball from Sandro.
Bolton fans were incensed but Van der Vaart was allowed to chip to Modric outside the area and the Croatian chested down before blasting a swerving shot into the top corner.
Bolton should have been level before the break.
Eagles first shot wide with a long-range effort before Boyata put a golden opportunity over the bar from a stoppage-time corner.
Bolton had a scare early in the second half as David Wheater gifted possession to Van der Vaart but Tim Ream snuffed out the counter-attack.
The Trotters pulled themselves back level with a well-worked equaliser in the 51st minute.
Kevin Davies headed on Boyata's throw-in to Ngog and his backheel rolled perfectly for Reo-Coker, who fired a low shot past Friedel.
The goal lifted the crowd and Bolton upped the tempo.
Petrov found himself in a good position but scuffed a shot wide and three corners in quick succession caused some anxiety in the Spurs box.
Eagles was the next to take aim after another throw was hurled into the area but his effort went narrowly over.
Bolton paid for their failure to make the most of that spell as Spurs launched two quick counter-raids to score twice in as many minutes.
Bale first stretched the defence and Van der Vaart finished brilliantly as the Welshman slid an inviting ball into his path.
Barely seconds later, Lennon got behind the defence as he raced on to a long ball from Modric and squared for Adebayor to tap home.
Bolton briefly rallied but the game was put beyond their reach as Bale sent Adebayor clear and the on-loan Manchester City striker casually rounded Bogdan to score.
Tensions were evident as Bolton substitute Josh Vela crudely brought down Aaron Lennon, sparking a row on the touchlines between Spurs assistant boss Joe Jordan and Bolton manager Owen Coyle.
Redknapp appeared to step in as peacemaker and Vela was booked.
Bolton endured more frustration as Petrov crossed and both Kevin Davies and Eagles failed to trouble Friedel.
Adebayor tried his luck from distance in search of a hat-trick but chipped over.
Spurs played out time to record their first win at the Reebok Stadium and the travelling fans chanted their support of Redknapp.