Gareth Southgate's side were far from their fluid best in the opening stages, but a third straight win in Group A never looked in doubt after Kane's opener in the 24th minute.
The Three Lions captain added a second from the penalty spot three minutes into the second half, before teeing up Raheem Sterling for a third.
Kane added another from the spot in the 73rd minute as England warmed up for Tuesday's visit of the group's surprise package, Kosovo, in style.
After a subdued start, Kane thought he had given the hosts a 19th-minute lead. The Tottenham striker had strayed into an offside position, however, before tucking away Raheem Sterling's pass from close range.
He was not to be denied five minutes later, though, taking full advantage of slapstick goalkeeping from Plamen Iliev to score his 23rd international goal.
After a short goal-kick, Iliev's attempted pass to Vasil Bozhikov was cut out by Sterling, who teed up Kane to stroke home from six yards.
Kane went close again shortly before the interval, heading straight at Iliev from Kieran Trippier's teasing right-wing cross.
Jordan Pickford kept out Wanderson's close-range effort a few moments after the restart, before a surging run from Marcus Rashford led to England's second.
The Manchester United forward was brought down in the area by Nikolay Bodurov, with Kane coolly stroking home the resulting spot-kick.
Kane turned provider for England's third in the 55th minute, crossing for Sterling to bundle home his ninth international goal from point-blank range.
The 26-year-old added gloss to a superb individual display 17 minutes from time, whipping in from the penalty spot after he had been clumsily brought down in the area by Kristian Dimitrov.
What does it mean? Southgate's side in rude health
They might have fallen one short of the five goals they plundered in each of their opening two group games, but England once again enjoyed themselves against limited opposition. They are top of Group A after three games and you would not back against them qualifying for next year's tournament without dropping points.
Kane proves he is more than able
The talismanic striker made light of suggestions he has started the season short of full fitness, delivering a masterclass in how to lead the line. Not only did he find the back of the net three times, but he also superbly picked out Sterling for England's third.
Iliev's lapse proves costly
Bulgaria will be left to rue Iliev's moment of madness. They were holding England at bay with something approaching relative ease, but their goalkeeper's misplaced pass was ruthlessly punished to set Southgate's side on their way to a comfortable win.
England will hope to continue their fine start to qualifying when Kosovo – who have picked up eight points from their four games – visit Wembley on Tuesday, while Bulgaria's attentions turn to a friendly against the Republic of Ireland in Dublin on the same day.