The previously uncapped Tottenham forward dominated the build-up to the Wembley fixture, but was made to wait for a first start as he was named among the substitutes on Friday.
However, within 79 seconds of having come on as a 71st-minute replacement for captain Wayne Rooney, Kane had opened his England account by heading in from a Raheem Sterling cross.
England dominated from the off and, after hitting the post early on, Rooney broke the deadlock with a simple header.
Danny Welbeck's deflected second on the stroke of half-time gave England a well-earned cushion, before Sterling - scoring his first international goal - latched onto a low Rooney cross to make it 3-0 just short of the hour.
Kane's memorable fourth gave the victory added gloss, as England maintained their 100 per cent record after five games in Group E.
Watching on from the bench, Kane might have felt he could have done a better job than Rooney when the captain struck the left-hand post from a promising position after five minutes.
However, Rooney – closing in on Bobby Charlton's record of 49 goals for England – made amends by heading in two minutes later, after Giedrius Arlauskis' save from a Welbeck strike bounced up kindly for him.
The goal was Rooney's 47th in international football, taking him within one of second-placed Gary Lineker.
Lithuania had half-hearted appeals for handball in the penalty area turned down in the 16th minute, before Rooney was denied by the woodwork again – this time sending a looping header onto the crossbar.
England continued to dominate proceedings, but Phil Jones had to be alert to slide in and prevent Deivydas Matulevicius getting on the end of a low Vytautas Andriuskevicius ball in from the left.
The home side looked to be heading into the break with a narrow advantage until Welbeck's header from a Jordan Henderson cross found the net via the thigh of Lithuania skipper Tadas Kijanskas to earn England a deserved second.
Fabian Delph drew an excellent save from Arlauskis with a left-footed volley four minutes into the second half, before Welbeck had appeals for a penalty turned down after tumbling under the challenge of Kijanskas.
Rooney was central to much of England's attacking play throughout and was on hand to provide the assist as Sterling touched home from close range two minutes before the hour mark.
Kane - who has now scored 30 goals this season - got his chance in the 71st minute and wasted little time in announcing himself on the international stage, heading in from a Sterling cross to put the match to bed.
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