After a lively start from both sides, the closely-fought contest soon became a scrappy affair at the Amex, with Ipswich heading into half time after failing to register a single shot on goal and just one touch in the opposition's penalty box.
The best moment of the first 45 fell to Brighton 10 minutes before the break when Ipswich goalkeeper Arijanet Muric was forced into making a superb double save to deny Georginio Rutter's driven shot from inside the box and a rebound tapped towards goal by Kaoru Mitoma.
Ipswich livened up midway through the second half and came close to opening the scoring when summer signing Liam Delap powerfully drove towards goal and watched his shot on the slide smack the outside of the post.
Boasting 70% possession, Brighton attempted to turn the screw in the closing stages, but the Seagulls - without the presence of Joao Pedro in their side - ultimately lacked a cutting edge in the final third.
A share of the spoils means Fabian Hurzeler's men remain unbeaten after four Premier League games and sit third in the table, while Kieran McKenna's side are still searching for their first top-flight win and are down in 17th place, just one point above the bottom three.
BRIGHTON VS. IPSWICH HIGHLIGHTS
Arijanet Muric's double save vs. Brighton (35th min, Brighton 0-0 Ipswich)
Ipswich had Muric to thank for keeping the scores level towards the end of the first half when he made two vital stops to deny Rutter and Mitoma.
The former ran onto Yankuba Minteh's smart pass and saw his shot parried by Muric, before the Kosovan reacted well to keep out the rebound from Mitoma from six yards out.
Liam Delap hits post vs. Brighton (57th min, Brighton 0-0 Ipswich)
Against the run of play, Liam Delap broke forward and, without the presence of any teammates in support, continued has powerful run into the box before sliding a fierce shot against the post.
MAN OF THE MATCH - ARIJANET MURIC
Muric has made a name for himself for the wrong reasons at times as a Premier League goalkeeper with some error-strewn performances, but he stood firm to thwart the efforts that came his way against Brighton, making a total of six saves - including the vital aforementioned double save in the first half - to help Ipswich claim what could prove to be a valuable point.
BRIGHTON VS. IPSWICH MATCH STATS
Possession: Brighton 70%-30% Ipswich
Shots: Brighton 21-6 Ipswich
Shots on target: Brighton 6-1 Ipswich
Corners: Brighton 9-2 Ipswich
Fouls: Brighton 14-16 Ipswich
BEST STATS
WHAT NEXT?
Brighton will now turn their attention to the third round of the EFL Cup and a home encounter against fellow Premier League side Wolverhampton Wanderers next Wednesday.
As for Ipswich, who were eliminated from the EFL Cup on penalties by AFC Wimbledon last month, they are next in action on September 21 when they travel to St Mary's to face Southampton in the Premier League.