Spurs were frustrated not to have scored themselves when things went very wrong.
Paulinho nodded home from a corner and then, with virtually the last kick, Arthur Gomes sauntered into the box to convert and put Sporting top of Group D with two wins from two.
Spurs boss Antonio Conte will be furious with the manner of the loss as his side suffered their first defeat since April in an uninspiring display.
Spurs thought they had taken the lead on the stroke of half-time as Richarlison rounded the goalkeeper after being played through by Harry Kane, but the Brazilian was well offside.
Hugo Lloris made a good save to deny Marcus Edwards a wonder goal after a dazzling dribble but Spurs were pressing for a winner when Sporting struck.
Paulinho glanced a header home before Arthur produced a moment of brilliance to weave into the area and shoot under Lloris.
Edin Dzeko scored one and created another as Inter Milan cruised to a 2-0 Group C victory over Viktoria Plzen.
Inter controlled the match and opened the scoring in the 20th minute when Joaquin Correa picked out an unmarked Dzeko, whose right-footed shot beat Plzen keeper Jindrich Stanek.
The Czech champions spent most of the game defending and faced an uphill battle after Pavel Bucha was sent off in the 61st minute for a dangerous tackle on Inter midfielder Nicolo Barella.
The visitors doubled their lead when Dzeko's clinical pass allowed Denzel Dumfries to slot home.
With agencies
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