Mikel Arteta's side had been hoping to build on an encouraging New Year's Day home win over Manchester United but they were left frustrated again and they have now won only one of the Spaniard's first five league games in charge.
Arsenal had a good shout for a penalty after the break when Nicolas Pepe went down in the area but VAR ruled in favour of the visitors, who then made the most of the let-off.
Fleck earned them a point late on when he beat Bernd Leno from close range in the 83rd minute as United ended strongly and could have even returned home with the win.
Chris Wilder's side remain four points and three places above Arsenal with 33 points from 23 games.
Arsenal, who enjoyed 61 percent possession but were well-shackled by the visitors, have 29 points and face a tough test at fourth-placed Chelsea in midweek.
Gabon striker Aubameyang has scored 47% of Arsenal's league goals this season and his absence blunted the attack, although Martinelli, in only his fourth league start, impressed.
He had already gone close with a volley from Pepe's cross and fired another effort into the side-netting before pouncing on Saka's looping cross into the area.
"Gabi's gonna be a superstar; not because of the goal because of the attitude energy and mindset," Aubameyang said on Twitter of his replacement's contribution.
It was Robinson's cross that was nodded on by Sharp for Fleck to bounce a shot past Leno.
"The result is better than the performance," Wilder said. "When teams don't put you to bed you always have a chance."