The young striker - on loan at Carrow Road this season - had been sidelined since September with an ankle injury but was back with a bang as the Canaries beat the Hammers 3-1 in the Barclays U21 Premier League.
Kane struck the post before opening the scoring in the first half, was then upended for a penalty converted by Olumide Durojaiye before tapping home his second and Norwich's third.
He had made only two appearances for the Canaries before his injury.
Adam Smith played another 90-minute shift for Millwall in Tuesday night's 2-2 draw at Brighton in the Championship. The Lions led 2-0 before Gus Poyet's men struck back in the second half.
Away from the UK, Bongani Khumalo played 90 minutes as PAOK beat Giannina 3-1 in the Greek Super League on Monday night. POAK remain second, eight points behind Olympiacos.
Adam Smith completed another 90-minute shift as the Lions beat Leicester City 1-0 at the New Den on Saturday to move back into the play-off places in the Championship.
Jordan Archer is also enjoying a successful loan spell in League Two at Wycombe and helped the Chairboys make it five matches unbeaten with a 2-0 win at Accrington Stanley on Saturday.
As well as the clean sheet, Jordan set-up one of the best chances of the game, his long clearance sent Bruno Andrade through on goal, but he was denied one-on-one by Stanley goalkeeper Paul Rachubka.
Meanwhile, John Bostock was an unused substitute as Swindon beat Oldham 2-0 in League One.