Manchester United went two points clear at the top of the Premier League after beating Chelsea in a highly eventful encounter at Old Trafford. The scoreline barely starts to tell the story of a game that was a mixture of madcap moments, missed opportunities and high quality that ended with Sir Alex Ferguson's champions maintaining their 100% league record. United were three up at half-time with goals from Chris Smalling, Nani and Wayne Rooney as Chelsea contributed to their own downfall courtesy of poor defending and a dismal failure to take the chances that came their way. Fernando Torres, lively throughout, scored his first goal of the season with a fine finish just after half-time but his improved performance will be scarred by his astonishing late miss at the Stretford End when he shot wide of an open goal after skipping around United goalkeeper David de Gea. It spared some embarrassment for Rooney, who earlier missed a penalty in farcical circumstances when he slipped haplessly as he ran up to take his kick. Rooney's misfortune did not prove costly though as United took advantage of another slip-up which came 200 miles away, when neighbours Manchester City blew a two-goal lead at Fulham. Chelsea manager Andre Villas-Boas suffered his first defeat since his arrival at Stamford Bridge - and his first league loss since his Academica side went down 3-2 at home to Benfica in Portugal in April 2010. He may take some comfort from the fact Chelsea held their own for long periods but were ultimately let down by moments of weakness at both ends. United have been devastating when offered opportunities this season. And so it proved when poor marking from Ashley Young's free-kick left Smalling unattended to head powerfully past Petr Cech, although the visitors felt he was offside. Chelsea were not discouraged by the early setback though and wasted two chances to equalise before the game was taken out of their reach in the closing stages of the first half. Torres scuffed an angled finish after Anderson carelessly conceded possession and another culprit was Ramires, who was guilty of an awful miss in the 25th minute. The impressive Juan Mata played in Torres, who unselfishly squared the ball for Ramires in front of an open goal, but his weak finish allowed De Gea to make a scrambling save. Chelsea paid a huge price for Ramires' generosity as United struck twice before half-time to put themselves firmly in control. Nani scored the second with a spectacular rising drive from the edge of the area nine minutes before the interval and Rooney, inevitably, was the man on the spot as United increased their lead in the closing seconds of the half. John Terry's clearance struck Nani and rolled invitingly into Rooney's path for the simplest of finishes. It prompted Villas-Boas into making a change with Nicolas Anelka coming on to replace Frank Lampard - a switch that had an instant impact as the Frenchman played in Torres within a minute of the restart for the sort of finish that was his trademark at the height of his powers. Chelsea suddenly had hope but it looked to have been snatched away when United were awarded a penalty in the 55th minute. Nani struck the bar after cutting inside and was then hauled down by Bosingwa as he chased the rebound. Rooney exchanged smiles with England colleague Terry as he waited to run up but Chelsea's captain had the last laugh as the striker slipped as he took the kick and missed the target. Torres was showing real signs of sharpness, meanwhile, as he brought another save from De Gea, but Rooney was also in the mood and rolled an effort against the foot of the post with Cech beaten. There was no excuse for Torres, however, when he somehow failed to score his second with seven minutes left. He sidestepped De Gea with ease and composure at the Stretford End then, with an open goal at his mercy, missed the target hopelessly as the taunts for the former Liverpool striker rang around Old Trafford. The action continued right until the final whistle as Cole cleared off the line from United substitute Dimitar Berbatov after he was set up by Rooney.