Tomas Soucek inadvertently turned into his own net in the 64th minute to give Spurs the lead and Kane, who finally returned from a hamstring injury suffered in January in Friday's draw with Manchester United, made sure of the result on his 200th league appearance for the club.
Victory for Jose Mourinho's men keeps the pressure on Manchester United and Wolves as they seek to return to the Champions League following their last-16 exit this season.
Meanwhile, West Ham remain outside the bottom three only on goal difference having suffered successive defeats since the season resumed after the coronavirus-enforced hiatus.