The Yorkshire club had lost all six league games on their travels ahead of the game at Portman Road and were heading for another defeat when Daryl Murphy gave Ipswich the lead late in the first half.
Winger O’Brien, on as a first-half substitute for the injured Jacob Mellis, denied Mick McCarthy’s side all three points with an equaliser 20 minutes from time.
Ipswich left-back Aaron Cresswell was sent off for foul and abusive language in the tunnel after the game on a frustrating night for the home side.
David Flitcroft’s charges remain in the relegation zone but move up a place to 22nd, while Ipswich are 10th.
In the other Football League game on Friday evening, Southend United responded to back-to-back defeats by beating Mansfield Town 3-0 in a League Two clash at Roots Hall featuring a trio of red cards.
Anthony Straker opened the scoring before Mansfield forward James Alabi and Southend's Conor Clifford saw red, and a Jamie McGuire own goal gave the hosts breathing space prior to half-time.
Mansfield defender Lee Beevers was sent off for a second bookable offence in the 90th minute and Kevan Hurst rubbed salt into the beaten side's wounds by adding a third goal.
Phil Brown's side are up to eighth and level on points with seventh-placed Newport County, while Mansfield missed the opportunity to move into the play-off places and occupy 12th.
‘Maybe I’ll be signed by Wrexham, who knows? English football would suit me – if an offer came, I wouldn’t think twice, I’d go immediately’ Euro 2024 cult hero reveals his UK dream
‘Managing Leeds? It was an option that appeared, but it wasn’t the right timing. I decided it wasn’t a good idea to leave the club I was at mid-season’: Premier League boss admits to turning down opportunity to replace Jesse Marsch in 2023
