Barry rises late to snatch points for City December 22, 2012 -- Updated 1936 GMT (0336 HKT) Gareth Barry scores the winner against Reading at a rainy Etihad Stadium to close gap on Manchester United to three points. England midfielder heads home an injury-time winner to keep Man City in touching distance of leaders United Arsenal up to third with a 1-0 at Wigan; Everton up to fourth after beating West Ham 2-1 English Premier League entering busy Christmas with most teams playing three games in six days (CNN) -- A 92nd minute goal by Gareth Barry earned Manchester City a valuable three points against bottom-of-the-table Reading at the Etihad Stadium on Saturday as the English Premier League heads into a busy Christmas period. The England midfielder headed in David Silva's cross to snatch the win which sees them move to within three points of leaders Manchester United who travel to Swansea City on Sunday. Like all Premier League teams, Roberto Mancini's team will play three games over the Christmas and New Year period. First up will be Sunderland on Boxing Day followed by Norwich City -- both matches away -- before City return to the Etihad on New Year's Day to face Stoke City. Following Sunday's matches at the Liberty Stadium, title rivals United entertain Newcastle and West Bromwich Albion before traveling to Wigan on January 1. Roberto Martinez's men, who famously dented United's title challenge at the DW Stadium last April, lost to Arsenal 1-0 on Saturday. Mikel Arteta's 60th minute penalty gives Arsene Wenger's side their third straight league win and moves them up to third place with 30 points, level with North London rivals Tottenham Hotspur who drew 0-0 against Stoke at White Hart Lane. The result means Spurs slip to fifth on goal difference below both Arsenal and Everton who also picked up three away points beating West Ham 2-1 at Upton Park. Second-half goals from Victor Anichebe and Steven Pienaar (64th and 73rd minute) clinched the win after Carlton Cole gave the Hammers the lead in the 14th minute. West Brom complete the quartet of clubs on 30 points after they came from behind to beat Norwich 2-1 at the Hawthorns. Zoltan Gera (43rd minute) and Romelu Lukaku (82nd minute) were on target after a Robert Snodgrass free kick gave the visitors the lead in the 23rd minute. Liverpool enjoyed a comprehensive 4-0 win against Fulham at Anfield. Martin Skrtel and Steven Gerrard were on target in the first half before second-half strikes from Stewart Downing and Luis Suarez completed a miserable day on Merseyside for Martin Jol's team. The win takes Liverpool up eighth on 25 points, four points behind Rafa Benitez's Chelsea who entertain Aston Villa on Sunday. Fulham remain in 13th on 20 points. Elsewhere, Shola Ameobi earned Newcastle a vital 1-0 win against relegation-threatened Queens Park Rangers while Sunderland also eased the pressure on manager Martin O'Neill with a 1-0 at Southampton. The win lifts the Black Cats to 15th with 19 points with the Magpies one point and one place above them.