There were few scoring chances in a passionate affair at Highbury, with the two sides packing midfield and seeming to worry more about avoiding defeat than taking maximum points.
Second-placed United will have more regrets, though, after the draw left them 13 points behind runaway leaders Chelsea.
Arsenal's title hopes were realistically already over, they now trail Chelsea by a whopping 24 points in fifth position.
There were goalmouth melees at both ends in the closing minutes while Arsenal had a penalty appeal waved away when Spanish midfielder Cesc Fabregas went down under a challenge by United's England defender Gary Neville.
But the spectacle fell short of what had been expected between two sides whose encounters had become the sharpest in English football.
Their last league meeting at Highbury before Arsenal move to the Emirates Stadium next season was also their first since both former captains moved on, Arsenal's Patrick Vieira to Juventus and United's Roy Keane to Celtic.
Arsenal, starting with an unfamiliar five-man midfield and Thierry Henry as a lone striker, applied the early pressure without carving any clearcut chances.
Alexander Hleb miskicked an early Robert Pires cross while Fabregas shot wide from the edge of the area after United tried to clear an Henry free kick.
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If Arsenal were lacking a killer pass, United were missing the inventiveness of the absent Paul Scholes and Wayne Rooney's usual creative spark. Yet they still conjured up the best scoring chance in a spell of pressure before halftime.
BALLOONED CHANCE
Ruud van Nistelrooy unleashed a searing shot that Jens Lehmann could only parry and Cristiano Ronaldo, who scored twice when United won 4-2 here last season, ballooned his follow-up over the bar.
Buoyed by their flourish, United looked the better side after the break, intent on revenge after last season's penalty shootout defeat by Arsenal in the FA Cup final.
Ronaldo sent in several telling crosses, van Nistelrooy found more time and space and Rooney showed neat flicks.
Arsenal manager Arsene Wenger threw on Dutch forward Dennis Bergkamp in search of a late winner but it was United who nearly had the final say when Wes Brown's effort was cleared off the line.
Though the rivalry stretches back to a mass brawl at Old Trafford in 1990, there has been no shortage of fireworks in recent years.
A United home win in October 2004 which ended Arsenal's record-breaking league run at 49 matches was followed by the so-called "Battle of the Buffet" when bits of pizza were allegedly thrown at United manager Alex Ferguson in the players' tunnel.
Four Arsenal players were banned and the club fined following ugly scenes at the end of another Old Trafford encounter which finished 0-0 early in that run in September 2003.