The 81-year-old fan suffered a cardiac arrest during the Premier League match at White Hart Lane and later died in hospital after being first treated inside the ground.
"The club can confirm that an 81-year-old male fan suffered a heart attack at last night's Premier League match against West Bromwich Albion," a Tottenham spokesman said Wednesday.
"We have since received confirmation that he later died in hospital.
"Our thoughts are with his family at this sad time."
England striker Jermain Defoe, who scored the only goal of a 1-0 victory in the 63rd minute, wrote on Twitter: "RIP to the fan that sadly passed away at last night's game. Condolences to all his family."
Tottenham's victory left them third in the table, six points behind leaders Manchester City but with a game in hand.
It is more than 50 years since the north London club won the English title, with a team managed by Bill Nicholson winning both the old First Division and the FA Cup during Spurs' 'double' season of 1960/61.
Source: AFP
Source: AFP