Harry Kane gave Spurs the lead from the penalty spot but Brighton battled back and deservedly levelled in the second half thanks to Tariq Lamptey's first goal for Brighton.
Albion looked to be heading for a point but Gareth Bale came off the bench and headed home a winner on 73 minutes.
Somewhat harsh on Brighton who changed shape and personnel for this one and looked better for it. Lamptey was once again excellent and there was also an encouraging debut in goal for 6ft 6in Spaniard Robert Sanchez.
Scroll down and click through to see how they rated.
1. Robert Sanchez 7/10
Tipped over an early effort from Reguilon to settle the nerves on his debut. No chance with Harry Kane's penalty or Gareth Bale's header. A great save to prevent a Veltman own goal. Took no risks with his distribution. Solid debut and given Maty Ryan and Potter plenty to ponder
2. Adam Webster 6/10
Skipper once more in Dunk's absence. Solid overall defensively and a couple of nice surging runs to get Albion moving forward. Lost Bale in the box for the header.
3. Joel Veltman 7/10
Looked very good at the back. Nice and composed in possession and took up good defensive positions. Solid match from the Dutch international
4. Dan Burn 6/10
Received a soft booking on the stroke of halftime for a challenge on Lamela.