United twice had to come from behind in a pulsating clash at the Madejski Stadium with all seven goals coming in the opening 34 minutes.
Hal Robson-Kanu opened the scoring with Reading's first meaningful attack after just eight minutes as he coolly volleyed home.
But United were level five-minutes later when Anderson beat Adam Federici at his near post after a lovely one-two with Ashley Young.
On the quarter-hour mark, the visitors were ahead after Jay Tabb inexplicably barged Jonny Evans in the back in the box and Wayne Rooney slotted home the resulting penalty.
The goals continued to flow and United's shaky-looking defence was breached again - this time Adam Le Fondre heading home unmarked from a Nicky Shorey corner.
Shorey was again the provider on 23 minutes as he curled in another corner, allowing young defender Sean Morrison to rise above Evans and head home solidly.
United, though, were not finished and on the half-hour they levelled when Patrice Evra broke on the left and cut the ball back into the area where Reading had left Rooney free to slot home from 10 yards.
Despite levelling - Sir Alex Ferguson was far from happy and he brought off Rafael to be replaced by Chris Smalling. The Brazilian's dissatisfaction was clear but he did eventually take his place on the bench.
Rooney then created what proved to be the winner 10 minutes before the break. A slick passing move involving Michael Carrick culminated in Rooney locating Robin van Persie's perfect run, and the Dutchman swept home with minimal fuss.
United should have had another just before the break. Young crossed to the back post for Smalling, whose header was blocked by Federici only for Van Persie to fire in the rebound - the referee's assistant incorrectly deciding Shaun Cummings had prevented the ball crossing the line.
The second half proved a real anti-climax with barely a chance to talk of, although Van Persie should have scored when he robbed the ball from a dallying Federici but could not hit the empty net from a narrowing angle.
Reading pushed on in stoppage time and a Morrison header was tipped over by Anders Lindegaard - the same player heading wide from the resulting corner as United held on to hoist their flag at the summit of the Premier League.