Ryan Sessegnon put the visitors ahead with a brilliant strike in the 55th minute. Fulham looked set for Arbeloa's first league win. Then they collapsed, and Abdoul Ouattara leveled in the 88th minute with a thunderbolt from 30 yards.
Dara O'Shea won it in the second minute of stoppage time, heading home Jack Clarke's free-kick.
Fulham now face another week in the relegation zone, seven points behind newly promoted Ipswich. It is the fourth league loss of the season for Arbeloa, a former Real Madrid manager. He walked straight down the tunnel at full-time after shaking hands with Ipswich boss Gary O'Neil. Asked about the pressure, he pushed back. "I never worry about my position," he said. "It's not about my position, it is about Fulham's position." He added that pressure has been part of his life since he was a kid, and that he likes it. "Obviously it is just six games, but it is true we need points." Hull visits Craven Cottage on Saturday.