A penalty from Tomer Hemed earned Chris Hughton’s men a point after an early opener from Luke Chambers but despite seeing striker Glenn Murray hit the bar in the 90th minute they couldn’t find a winner.
The result means Albion, who have won just one of their last four league games, are still one point behind leaders Newcastle.
And it also leaves third-placed Huddersfield, who won at Rotherham, starting to close in on the top two.
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Ipswich, however, were not going to make it easy for them.
Mick McCarthy’s men had five men booked in the first half alone but were competitive in attacking areas too.
Live ware Lawrence forced Stockdale into a fine save soon after the break. And then Chambers almost grabbed himself a second goal when he scraped the ball against the post from Jordan Spence’s header.
Ipswich took the lead through Luke Chambers
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Brighton levelled through Tomer Hemed
Hemed now has 16 goals for Brighton this season
In the melee that followed, Steve Sidwell headed off the line from McGoldrick and Brighton were clearly hanging on.
Hughton’s men finished strongly, with Sam Baldock going close and sub Murray hitting the bar right at the death. But they couldn’t find a winner.