The Red Devils capitalised after Manchester City were held by Everton earlier in the day with Anderson netting one of seven first-half goals in an incredible opening period
Manchester United pulled three points clear of rivals Manchester City at the top of the Premier League table as goals from Anderson, Robin van Persie and two from Wayne Rooney secured a 4-3 victory against Reading.
All seven strikes came in a quite remarkable first half of football, with both sides swapping the lead before Rooney, with his second, and Van Persie both found the net to score the goals that ultimately secured the three points for the visitors.
The Royals, who were unchanged, took an early lead as Jobi McAnuff's in-swinging cross from the left was only partially cleared by Jonny Evans and Hal Robson-Kanu capitalised on the loose ball, hammering an effort high into the far corner past a helpless Anders Lindegaard.
United's response, however, was immediate and lethal. Just four minutes after Robson-Kanu's strike Anderson raced onto Ashley Young's through ball and lashed past Federici to pull Sir Alex's men level with a second to follow shortly after.
Referee Mark Halsey pointed to the spot after Evans was bundled over in the area by Jay Tabb and Rooney stepped up and duly answered his manager's call for more goals by slamming the ball into the far corner, sending Federici the wrong way.
This astonishing first half witnessed a further twist, however, as the pendulum swung back in Reading's favour courtesy of two quick-fire goals from corners.
Nicky Shorey's pin-point deliveries from the right-hand-side were powerfully headed home with, firstly, Adam Le Fondre getting on the scoresheet a day before his 26th birthday before Sean Morrison climbed above Evans to make it 3-2 Reading.
The first-half drama ceased to reach a conclusion there, though, and United once again hit back to equalise. Young and Patrice Evra linked up superbly well on the left-hand-side before the latter squared for Rooney to bury from close range.
And, to the astonishment of everyone in the ground, the goals kept on coming. Sir Alex's side once again regaining the lead as, after 34 minutes, Van Persie latched onto Michael Carrick's through ball and slotted home his 10th league goal of the campaign with supreme composure.
The Dutch striker was unfortunate not to add to his tally before half-time as his close-range effort was cleared from underneath the crossbar but replays suggested that the ball had, in fact, crossed the line.
A comparatively dull start to the second half saw United slow the tempo although there were shouts for a penalty from the home support as Adrian Mariappa fell to the ground under a challenge from Evra but the Frenchman got just enough of a foot on the ball and no spot-kick forthcame.
Van Persie then wasted a glorious chance to grab his second of the match as he amazingly fired wide after robbing Federici.
The former Arsenal striker closed down the Reading goalkeeper and looked certain to make it 5-3 although, almost replicating Fernando Torres' infamous miss against the Red Devils, smashed his shot off target with Ferderici scrambling and the goal gaping.
Reading continued to pour forward in search of an equaliser although rarely troubled Lindegaard in the second period, with Tabb clearing the bar before Morrison forced the United goalkeeper to tip over in stoppage time.
The result moves Sir Alex's side three points clear of City with next weekend's Manchester derby looking increasingly pivotal while the Royals remain in the drop zone.