March's effort sent Brighton ahead in the 63rd minute, but Tomkins came up with the leveller seven minutes later, as the two teams shared the spoils in the Premier League contest.
The result has left Palace in 12th position in the table, boasting 25 points from their 22 matches, while Brighton sit sixth, moving onto 35 points from 21 league games this term.
Brighton had the first serous chance of the match in the 11th minute, with March setting up Alexis Mac Allister inside the penalty box, but the World Cup winner's low effort was saved by Vicente Guaita.
Palace's goalkeeper had to make another smart save in the 18th minute to keep out Mac Allister, with the Argentina international causing problems with his movement in the forward areas.
Guaita then made his third impressive stop of the half in the 27th minute, with the experienced goalkeeper keeping out Kaoru Mitoma, who had combined with March before looking to pick out the back of the net.
Brighton thought that they had made the breakthrough in the 32nd minute when Pervis Estupinan curled one into the top corner after smart work from Pascal Gross.
However, VAR came to Palace's rescue, with Estupinan in an offside position for the visitors.
There were two more chances before the end of the first period, with Jean-Philippe Mateta having a shot blocked by Adam Webster before Mac Allister had a shot deflected wide of the post down the other end.
Brighton managed to take the lead in the 63rd minute of the contest through March, who smashed the ball into the back of the net after being found by Estupinan.
The away side's lead only lasted seven minutes, though, with Tomkins levelling the scores in the 70th minute when he tapped home from close range after Robert Sanchez had failed to claim a Michael Olise free kick.
Mac Allister came close to sending Brighton 2-1 ahead in the 84th minute when he met a corner from Gross, but the Argentine's header dropped just wide of the post.
The attacker had another brilliant chance in the final minute after Estupinan had picked him out, but his volley was straight into the arms of the Palace goalkeeper, and the final whistle blew four minutes later with the two teams level at 1-1.
Next up for Palace is a trip to Brentford next Saturday, while Brighton will be bidding to return to winning ways when they welcome Fulham on the same afternoon.