Back in a holding role after recent outings at right-back, Teemu protected the back four, closing down and snapping away until he ran himself out in the second half and was replaced by Jamie O'Hara.
His display contributed to a clean sheet as Robbie Keane's 15th-minute goal secured a trip to Manchester United in the fourth round.
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"In the first 25 minutes our game was perfect," beamed coach Gus at Spurs Lodge on Wednesday. "That’s the sort of start we are looking for.
"We controlled the ball, passed it around, created chances, scored a goal and Teemu was managing all that in central midfield, controlling the whole game.
"He was outstanding and knew exactly what we wanted from him. He was tired at the end and that's why we changed it but we know how much eh enjoyed it out there. JJ was magnificent as well and everyone did their jobs.
"Chris Gunter played his first game and we asked him to be as calm as possible - sometimes that’s difficult because it’s your debut and you have to be a little nervous, but he coped well.
"We were very pleased with the performance, especially the clean sheet."
As for United next, Gus added: "It’s perfect for us, perfect. I know everyone would rather play a smaller team at home rather than the biggest team away but - I said it before - we have nothing to lose. We go to a place where the home team is doing fantastically well but we know we can win the game. We have to make sure our plan works and maybe we’ll come home happy from Manchester."
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Gus Poyet was full of praise for Teemu Tainio after the midfielder pulled the strings in Tuesday night's FA Cup replay win at Reading.