Ipswich's last top flight points came in a 1-0 win over Middlesbrough in April 2002
Ipswich Town earned their first point after returning to the Premier League, but could not force a win over Fulham in a scrappy encounter at Portman Road.
Liam Delap's fine shot in the 15th minute gave the hosts the lead for the forward's first goal since his summer transfer from Manchester City.
But the impressive Adama Traore levelled for Fulham when he drilled in a low strike before half-time.
Fulham goalkeeper Bernd Leno made several important saves after the break to deny Ipswich their first win in the top flight since April 2002.
Leno's fingertips took a deflected Delap shot away from the target, and he dived at the feet of Chiedozie Ogbene before blocking Omari Hutchinson's effort deep into injury time.
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Ipswich finished strongly to claim a gritty draw following a tough start to the season, which saw them lose at home to Liverpool and then away to champions Manchester City.
The result lifted Kieran McKenna's side out of the bottom three, while Fulham lay in 11th place on four points from three games.
Ipswich show spirit after tough start
Far from disgraced in their opening two league games, Ipswich were nevertheless under threat of two straight home defeats for the first time under McKenna before kick-off.
Factor in a dispiriting defeat on penalties to AFC Wimbledon in the EFL Cup in midweek and a nervous opening would have been understandable.
Delap lifted the mood with an excellent run and shot that burst through Leno's hands, but Ipswich went into their shell for much of the rest of the first half.
Kalvin Phillips made his first start in the league since arriving on loan from City, having been prevented from playing against his parent club, and lasted 70 minutes before being substituted.
Phillips and another summer arrival in Ogbene contributed to an energetic Ipswich performance, especially after the break when McKenna's outfit were chasing a win against a side largely content to sit back.
Delap continued to be a threat, but Ipswich will need to take their chances in what is sure to be a tough season.
"It is a step in the right direction, and so was the performance," Ipswich manager Kieran McKenna told BBC Match of the Day.
"We are adapting to the level, improving all the time and integrating players all the time, today we had six players who have joined us this summer.
"We were competing against a well-established team at this level so to compete how we did is a positive and we feel we have lots to come.
"Some of our pressing in the first half was excellent, and the organisation and discipline against a team that can give you problems was really, really good."
Cottagers fail to convert chances
Going a goal behind after a quarter of an hour provoked Marco Silva's side into action, and they deservedly equalised 17 minutes later.
Antonee Robinson's low cross from the left was met perfectly by Traore, giving the 28-year-old just his third goal since his arrival at Craven Cottage just over a year ago.
Rodrigo Muniz, Emile Smith Rowe, Alex Iwobi and Raul Jimenez all had chances, but the Ipswich goal was never under sustained threat.
The draw preserved their record of never winning more than one of their opening three games in the Premier League since 2008.
"The reaction from us was good, we scored a good equaliser and after that we took a step forward and were completely in control," Silva reflected to BBC Match of the Day.
"The second half was a lot more difficult for us, we were not able to control the game the way we liked. We were solid, we did not give many things but we did not create.
"We should create a lot more when we are on the ball, we have to be more effective in our build up and have more chances to score."
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