The England international flapped unconvincingly at a Blackpool corner and then sliced a kick as he came charging out to clear a long ball.
But Robinson did at least set up the opener, providing the long ball for Berbatov to head on, leaving Keane to score his ninth goal of the season.
Simon Grayson's Championship side came out in the second-half determined to make Spurs sweat and they did.
Taylor-Fletcher was desperately unlucky with a header which smacked against the bar and then Robinson boosted his confidence with a fine save as the striker's shot headed for the top corner.
But Tottenham's second sucked the life out of the visitors and substitute Jermain Defoe almost scored with his first touch, only for Rachubka to tip over the crossbar.
Tottenham boss Juande Ramos: "The most important thing was the win.
"The team needs to improve in all areas, in attack and defence, but this is a team of great professionals and I hope it will improve quickly.
"They've shown great willingness to play and fought very hard."
Blackpool boss Simon Grayson: "We had opportunities to get in front or to get back in the game but we didn't take them.
"We gave a good account of ourselves but they took their chances.
"Full credit to Juande Ramos. He came to speak to me at the hotel."
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