Harry Redknapp's side on Sunday condemned the Gunners to their fourth defeat in seven Premier League games this season after Arsenal goalkeeper Wojciech Szczesny failed to deal with Walker's swerving 30-yard effort in the 73rd minute at White Hart Lane.
Sixth-placed Spurs had taken the lead through Rafael van der Vaart's cool finish in the 40th minute, although the Dutch midfielder appeared to use the upper part of his arm to control Emmanuel Adebayor's pass prior to the goal.
Arsenal equalised in the 51st minute when Wales midfielder Aaron Ramsey finished off Alex Song's cross from close-range, but Walker settled a fiercely-fought derby when his shot slipped through Szczesny's grasp.
There was more bad news for Arsenal boss Arsene Wenger, whose side are languishing just two points off the relegation zone in 15th place, as France right-back Bacary Sagna was stretchered off in the second half.
At the Reebok Stadium, Lampard showed he still has plenty to offer with the sixth treble of his career as Andre Villas-Boas''s side routed bottom of the table Bolton, who have now lost six successive matches, to move back into third place, three points behind leaders Manchester United.
"It was good for him," Villas-Boas said. "He arrived with perfect timing into the box as he has done in the past years.
His talent was never in question.
"It is not a question of age - it is a question of competence, and this squad is full of competence."
The Blues took the lead after just 92 seconds when Daniel Sturridge, who enjoyed a successful loan spell at Bolton last season, punished poor marking to head Juan Mata''s corner past Adam Bogdan.