Mauricio Pochettino's side were in front after just five minutes following some poor defending, before the winger completed the scoring late on, displaying a typical burst of pace
Lewis Holtby capitalised on a defensive error to square for Kane, who tapped in the opener early on in the first half.
And Lennon completed the scoring in the closing stages, beating Chicago goalkeeper Sean Johnson before tapping into an empty net.
Chicago's coach Frank Yallop would have been furious with his team's start, as they gave up possession on the edge of their penalty area in just the fourth minute, allowing Kane to score.
But the Fire worked their way back into the contest as the half wore on with Matt Watson testing Tottenham keeper Brad Friedel in the 25th minute.
As the clock ticked past the half-hour mark, Tottenham midfielder Erik Lamela continued his strong close-season, skipping past a couple of opponents before forcing Chicago goalkeeper Sean Johnson into a fine save.
Lamela, who scored twice in a 3-2 win over Toronto FC on Wednesday, was at it again four minutes later, surging through midfield before a flying Johnson again kept the Argentine's shot from finishing in the net.
The hosts looked more comfortable after half-time, taking advantage of a number of substitutions from Pochettino, although Chicago struggled to fashion genuine goal-scoring chances in the first 20 minutes of the second period.
In the 69th minute, the Fire's Dilly Duka linked up with a couple of team-mates to work his way through Tottenham's midfield before his shot was saved lowdown by Friedel, while Chicago striker Matthew Fondy got into the box with 15 minutes left only to have his shot blocked.
Tottenham finished the match stronger with Lennon doubling their lead before Christian Eriksen got in behind the Fire's defence only for Reynish to smother his shot on the edge of the area.