LONDON — Premier League champion Manchester City remained seven points adrift of leader Manchester United after a 2-0 win away to Arsenal Sunday, with both teams finishing a man down in an eventful match. First-half goals from James Milner and Edin Dzeko put City in a commanding position against Arsenal, already down to 10 men after Laurent Koscielny was sent off in the 10th minute for bringing down Dzeko inside the box. Although Dzeko's penalty following Koscielny's red card was turned onto the post by Wojciech Szczesny, with the Arsenal goalkeeper gathering the rebound, it was not long before Milner and Dzeko himself made the man advantage count. The visitors too were a man down at the Emirates Stadium when, 15 minutes from time, City captain Vincent Kompany was dismissed by referee Mike Dean for a challenge on Jack Wilshere despite appearing to win the ball first. Second-placed City was briefly 10 points adrift of United after its cross-town rival beat Liverpool 2-1 at Old Trafford earlier in the day. Robin van Persie's league-high 17th goal of the campaign gave United a 19th-minute lead, and the host looked likely to coast to victory at Old Trafford when captain Nemanja Vidic bundled the ball in to make it 2-0 in the 54th. Daniel Sturridge, who came on as a halftime substitute, halved the deficit three minutes later but Liverpool couldn't find the equalizer to cap its improved second-half display. The game between England's two most successful clubs, which share 37 league titles between them, was billed by some as a duel between Van Persie and Liverpool striker Luis Suarez — the division's most prolific marksmen. Van Persie came out on top. While Suarez was kept quiet — much to the delight of home fans who jeered his every touch — his rival continued his sensational scoring run that is keeping City at arm's length in the title race. The Netherlands striker beat marker Daniel Agger to Patrice Evra's driven cross and calmly slotted the ball home from 12 yards for his ninth goal in his last nine games. Van Persie has also scored at least one goal in nine of his last 10 games. With Liverpool's midfield giving the ball away cheaply and sitting far too deep, United was invited to attack at will and should have been more than a goal ahead at halftime. Danny Welbeck, given a rare start up front with Wayne Rooney still injured, thrashed wildly wide and Tom Cleverley went close with a volley. Van Persie then saw an impudent flick cleared from near the goal-line by Liverpool defender Martin Skrtel before Pepe Reina pushed the ball away from the inrushing Shinji Kagawa. The first half highlighted the gap that has emerged between the two sides in recent years, with the last of Liverpool's 18 titles coming back in 1990. It was much different after the break, though. Sturridge was introduced for the second half for his league debut for Liverpool and his pace and energy sparked a vast improvement by the visitors, who finally tested the United defense. The former Chelsea striker's goal came only after United had stretched its lead, however, when Van Persie's free kick was headed down by the unmarked Evra with the ball deflecting off the side of Vidic's head into the net. Liverpool's riposte was almost immediate, Sturridge sidefooting home from close range after David De Gea could only palm out Steven Gerrard's low shot, and it set up a tense last half hour for the home side. Sturridge and fellow substitute Fabio Borini shot wide as United fans became increasingly anxious, and Sturridge had an even better opportunity in the 85th only to blaze over the crossbar from an angle. United is now 24 points clear of eighth-place Liverpool in the standings. — Agencies Standings P W D L F A Pts 1. Man United 22 18 1 3 56 29 55 2. Manchester City 22 14 6 2 43 19 48 3. Chelsea 21 12 5 4 43 19 41 4. Tottenham 22 12 4 6 39 27 40 5. Everton 22 9 10 3 35 26 37 6. Arsenal 21 9 7 5 40 24 34 7. West Bromwich 22 10 3 9 31 30 33 8. Liverpool 22 8 7 7 35 28 31 9. Swansea City 22 7 9 6 31 26 30 10. Stoke City 22 6 11 5 21 24 29 11. West Ham 21 7 5 9 24 27 26 12. Norwich City 22 6 8 8 24 34 26 13. Fulham 22 6 7 9 33 38 25 14. Sunderland 22 6 7 9 24 29 25 15. Southampton 21 5 6 10 28 38 21 16. Newcastle 22 5 6 11 27 39 21 17. Wigan Athletic 22 5 4 13 23 40 19 18. Aston Villa 22 4 7 11 17 42 19 19. Reading 22 3 7 12 26 42 16 20. QPR 22 2 8 12 17 36 14