The Seagulls, now only two points ahead of Ipswich, boasted 17 clean sheets going into the match and they came unstuck before a crowd of 29,093 - the biggest at the Amex Stadium this season.
Brighton, who went into the game with only one defeat in their previous 11 home games in all competitions, should have gone ahead in only the fifth minute when Jesse Lingard shot straight at keeper Dean Gerken after getting clean through.
The Seagulls' Polish keeper Tomasz Kuszczak saved a goal-bound shot from skipper Luke Chambers before Albion's leading scorer Leonardo Ulloa just failed to get on the end of a teasing cross from Bruno Saltor.
Brighton had a penalty appeal waved away when Lingard went over following a challenge by defender Christophe Berra.
Ulloa, bearing a heavy workload in attack with Craig Mackail-Smith and Will Hoskins not yet back following injury, was denied by Gerken after heading firmly towards goal after an excellent cross by Bruno.
Midfielder Jonny Williams, on loan from Crystal Palace, had the ball in the net for Ipswich mid-way through the first half but the effort was ruled out through off-side with Aaron Cresswell having initially burst down the left.
Lingard failed to test keeper Gerken when firing over from the edge of the area having carved out an opening by skilfully cutting in.
Ipswich went close through Cresswell, whose shot deflected off Bruno and the back-peddling Kuszczak was relieved to see the ball go just over the bar.
Good work from Will Buckley set Lingard up in front of goal, but he wastefully put a right-foot shot wide of Gerken's left-hand post.
Brighton made a fast start to the second half and from a cross by Ulloa, Stephen Ward had a shot blocked before Jake Forster-Caskey shot over at the far post.
Gerken kept Ipswich on level terms by diving to his right to keep out a low drive from Lingard.
Ipswich broke the deadlock on the hour when defender Smith scored for the second match running.
Keeper Kuszczak got caught underneath a corner from Stephen Hunt and it was headed back by Murphy for Smith to net from close range.
Ulloa almost levelled nine minutes later but his header from a cross by Lingard
flew narrowly wide.
Ipswich doubled their advantage 10 minutes from time through Murphy who neatly headed home from an assist by Williams.