United have won eight and drawn three of their last 11 Premiership matches, but they trail the runaway leaders by 13 points after this draw.
Arsenal are out of the race already and they face a struggle to overhaul Tottenham for England's fourth Champions League slot, ahead of their move to Ashburton Grove.
Arsenal have not beaten United in seven Premiership meetings and they rarely threatened to break the deadlock again. United had the best chances late in the second half, but could not take them.
This was a contest shorn of the gladiators of recent years, Patrick Vieira and Roy Keane. How the occasion needed their passion.
Arsenal were without Robin van Persie, Freddie Ljungberg, though Gilberto returned in midfield.
Ashley Cole is still out, so Pascal Cygan continued at left-back. United wanted Cristiano Ronaldo or Ryan Giggs to attack him at every opportunity and feed Ruud van Nistelrooy. Jose Antonio Reyes dropped deep to support the makeshift left-back.
The Gunners opened with an unfamiliar 4-5-1 formation to give strength in numbers and dominate possession. They did the early probing with Cesc Fabregas the prompter.
Wes Brown made an important tackle to halt Robert Pires and Aleksandr Hleb missed his kick as he tried to connect with Pires' cross. Fabregas hit a 20-yarder a foot wide after Darren Fletcher headed out a free-kick.
At the other end, Jens Lehmann rushed out of his goal to make an eighth-minute clearance from Wayne Rooney.
Edwin Van der Sar made the first save, from Pires' near-post shot after a clever flick by Thierry Henry. He was barely involved again.
The Gunners won a series of corners. Henry could not find his range with his inswingers to the far post, but he offered Arsenal's biggest threat. He hit a 31st-minute free-kick inches above the junction of post and bar.
United's central midfielders Darren Fletcher and John O'Shea were content to hold their positions. Arsenal weaved pretty patterns but lacked penetration. How they still lack an alternative when their clever football is frustrated.
United almost punished them in the 44th minute. Lehmann palmed out van Nistelrooy's blistering shot and Ronaldo lashed the rebound high and wide.
Arsenal needed more support for Henry. He still conjured a shot that forced a decisive block from Rio Ferdinand, before Brown blocked Gilberto's shot in a scramble.
Arsenal continued to trip up in their own intricacy. Meanwhile, United began to make chances of their own. Rooney headed across goal, too far in front of van Nistelrooy. Giggs missed his kick from Ronaldo's low centre.
Van Nistelrooy fired wide after a defensive mix-up and Rooney split the Arsenal defence, but Kolo Toure's last-ditch block denied the Dutchman.
Henry almost set up a decisive opening for Pires, then smashed wide after a surging run by Sol Campbell. Both half chances came from a more direct approach.
But the Gunners seemed reluctant to take chances in search of a winner and United seemed happy to take a point. Yet the visitors should have snatched a winner in the dying minutes.
Rooney's punt flicked off an Arsenal defender and the unmarked Gary Neville fired into the sidenetting. Sub Emmanuel Eboue then hacked away Brown's header from a stoppage time corner.