The first incursion happened shortly before Spurs made the game safe with their third goal of the night, with the second coming just before the full-time whistle.
It isn't the first time that West Ham's securty has come under scrutiny, with the club still waiting to discover if they will face charges from the FA following a pitch invasion and crowd trouble during the Premier League game against Burnley back in March.
The London Legacy Development Corporation (LLDC) controls the general management of the ground, for which West Ham pay £3m a year in rent, but the matchday operation of the stadium is farmed out to subsidiary LS185.
the security probvlems have led to debates over which parties should be expected to pay which running costs, with 'Hammers' vice-chairman Karren Brady suggesting that the club would like to take more control of the stadium on matchdays.