All five goals came in the first half as Wilfried Zaha bagged a couple and Tomkins added another, while Glenn Murray and Jose Izquierdo kept the Seagulls very much in the match.
The result left the Eagles 16th in the Premier League standings but, more importantly, opened up a six-point gap to the relegation zone.
Palace have turned their season around under Roy Hodgson after a dreadful start but also suffered a lengthy spell without a win in January and February.
The general consensus is that they were not playing badly but just unable to hang on for the right result, with many narrow losses.
And it is that aspect of Saturday’s win that pleases Tomkins the most.
‘It’s happened to us a few times when we have panicked towards the end but we managed to keep a clean sheet in the second half,’ he said.
‘We knew if we did that we would win the game but it was nerve wracking at times, and I can imagine the fans being a bit nervous watching us, but it’s three points which move us up the table and closer to safety.’
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