Albion lead Spurs after a scintillating first half which saw the Seagulls take the lead after just two minutes.
Neal Maupay scored from a header that left Spurs keeper Hugo Lloris fllored on the deck.
The Spurs keeper was stretchered off shortly afterwards.
Albion continued to have the upper hand with Aaron Mooy and Martin Montoya causing problems down the flanks.
Albion’s second was another close-range effort bundled home by Aaron Connolly as substitute keeper Paulo Grazzaniga spilt Mooy’s cross
Harry Kane and Christian Eriksen have so far hardly had a kick for Spurs.