Goalkeepers Jack Butland and Petr Cech were the star players, as they made excellent saves at both ends to ensure clean sheets for their team.
The brilliance of Butland stopped Arsenaal entering the half-time interval ahead as he spread himself to thwart Olivier Giroud in a one-on-one situation.
His heroics were then emulated by a man 11 years his senior as Cech kept out Joselu and Bojan Krkic in quick succession before saving with his feet from the former late on to record the 172nd Premier League clean sheet of his career.
The Gunners were without German midfielder Ozil, the man leading the Premier League in assists, due to a foot injury while Alexis Sanchez was not included either despite nearing a return from a hamstring problem.
A share of the spoils saw Arsenal return to the summit on goal difference ahead of surprise title contenders Leicester City, with both clubs now boasting 44 points from 22 league matches played so far this season.
In an Earlier match, Rooney — who made his name playing for Liverpool’s city rivals Everton — marked his latest return to Merseyside by scoring the only goal of the game at Anfield.
In his first game against United as Liverpool manager, Jurgen Klopp saw his team dominate only for Rooney to punish their wastefulness with his fifth goal in four games, a close range snapshot after Marouane Fellaini had hit the bar in the 78th minute proving the difference.
It was United’s only shot on target, but it was enough to give visiting manager Louis van Gaal his fourth win over Liverpool in four games and a first away victory since the 2-1 success at Watford on November 21.
The Victory took United to within two points of the Champions League berths and allowed them to reclaim fifth place from West Ham United, leaving Liverpool six points back in ninth place, their top-four hopes fading.