In 42 Premier League matches between the two clubs, there have only been three goalless draws (April 1995, December 1998, May 2007).
Chances were scarce with the home side just shading possession but failing to properly test Petr Cech in the Chelsea goal.
This was United’s first goalless home league game since they met Arsenal in May 2009.
In his first home game at the helm of the champions, David Moyes selected Wayne Rooney to partner Robin van Persie, despite rumours that he still may be wearing the blue of Chelsea before the transfer window slams shut on September 2.
Chants of "Rooney, Rooney!" rang out from both sets of supporters with the Chelsea fans singing: "We’ll see you next week!" in the direction of the England striker who put in an all-action performance.
The Reds went into the game having suffered 14 Premier League defeats against Chelsea — more than against any other side.
For Chelsea, victory would have ensured the west London club had claimed maximum points from their opening three league games in four of the last five seasons.
But the first game of the new season between two of the title rivals did little to showcase what the Premier League has to offer.
A cagey first half offered very little in the way of goalmouth action with the first real chance chance of the game falling to the away side. David de Gea, however, did well to adjust his feet and easily collect a snapshot from Oscar.
The home side, who just edged the possession stats, had their best chance after Michael Carrick closed down Ramires deep inside the Chelsea half. Van Persie picked up the ball just outside the box, tiptoed around Branislav Ivanovic and let fly with a fierce left-foot shot that hit the side-netting.
The second period offered just as little in the final third with United, again, just edging their visitors with ball possession.
United felt they should have been awarded a penalty midway through the half after Tom Cleverley’s shot struck Frank Lampard on the hand. Referee Martin Atkinson waved away any pleas from the United players — much to the frustration of the home supporters.
Gary Cahill had the Chelsea’s best effort of the half, but the defender's long-range strike was well saved by de Gea.
Jose Mourinho introduced Fernando Torres after 60 minutes, however the Spaniard failed to spark any life into the Chelsea forward line.
Moyes will hope for better from his charges when they travel to a ground he knows all too well on Sunday — Anfield — for another huge game for the former Everton manager.
Mourinho’s Chelsea are not back in league action until mid September as they will now travel to Prague to take on Bayern Munich in the Uefa Super Cup on Friday.