The Gunners, with a makeshift defence and missing Mesut Ozil because of a knee injury, took an early lead through Alexis Sanchez.
However, Hull hit back with a controversial equaliser from Mohamed Diame, as Arsenal claimed a foul in the build-up, and then took the lead at the start of the second half through Abel Hernandez, who had only been playing after an injury to Nikica Jelavic in the warm-up.
Arsenal, who lost Jack Wilshere to what could prove to be another ankle problem, pressed to get back into the match, but looked to have been frustrated until Welbeck slotted home in the first of six minutes of added time.
They then almost snatched the three points at the death through Kieran Gibbs, who was denied by stand-in Hull goalkeeper Eldin Jakupovic.
The Gunners made a bright start as Welbeck collected a ball up to the edge of the Hull penalty area and held off James Chester before rifling in an angled drive, which Steve Harper beat away and then was quick to block the follow-up from Sanchez.
Even better was to come from the Hull goalkeeper, though, as Harper acrobatically tipped over a curling 20-yard effort from Santi Cazorla at full stretch with one hand.
However, he could do little to prevent Arsenal sweeping into the lead on 13 minutes with a finish of the highest quality from Sanchez.
The Chile forward collected the ball on the right, and darted into the Hull penalty area before cutting back inside to drill a low shot across the goalkeeper into the far corner.
After Alex Oxlade-Chamberlain’s shot was blocked by Curtis Davies as the Arsenal players appealed for handball, Hull were level on 17 minutes when Diame picked the ball up some 25 yards out and barged past Monreal.
Mathieu Flamini then looked to have been pulled back by the midfielder, but referee Roger East allowed play to continue, with Diame clipping the ball over Wojciech Szczesny – much to the dismay of the Arsenal players and bench.
Arsenal looked to regain the initiative, having been in complete control before the controversial equaliser.
Hull dropped plenty of men behind the ball and proved difficult to break down in the final third.
There was a delay just before half-time when Harper needed treatment after collecting a pass-back and looked to have injured his shoulder or neck.
Veteran Swiss keeper Jakupovic came on and Hull snatched the lead right at the start of the second half.
Tom Huddlestone got clear on the right and floated a ball into the Arsenal penalty area, where Hernandez easily got in front of Per Mertesacker to power a header past Szczesny.
Once again Hull sat back, inviting Arsenal pressure, but the hosts continued to lack any spark in the final third.
With 26 minutes left, Hernandez was replaced by Gaston Ramirez, while Arsenal sent on Aaron Ramsey, out for several weeks with a hamstring injury.
Wilshere then hobbled off after looking to have jarred his ankle in a tackle with Ramirez, which earned him a yellow card. Costa Rica forward Joel Campbell came on.
Hull defender Michael Dawson went down in a heap at an Arsenal corner, but was able to continue only to then be forced off after blocking a goal-bound effort from Sanchez, who then saw a looping header tipped over by Jakupovic.
Just after the fourth official showed six minutes of added time, the Chilean skipped to the edge of the Hull area before slipping in Welbeck, who guided the ball into the far corner to equalise.
Arsenal poured forwards in search of a dramatic winner, with Jakupovic spilling a low shot from Cazorla and then blocked Gibb’s late run at the far post as Hull held out.
Matt Le Tissier’s verdict
“Hull did come close, but in the cold light of day Steve Bruce would probably accept that a point was a decent return for him. They were hanging on and hanging on and once they were 2-1 up they didn’t show any will to get forward again. They all sat back and invited Arsenal onto them – and Arsenal are so good, at the Emirates, at nicking late goals to save matches and that’s exactly what they did today. In the end, I think Steve Bruce will accept a point.
“It sounds silly when they’ve let in two goals, but Arsenal’s new-look defence didn’t have much to do. Hull just didn’t attack that much to test them out, really. There’s no way in the world the first Hull goal should have stood. It was a foul, one million per cent.”