FRANKFURT, Jan 29 (Reuters) - Werder Bremen scraped a 1-0 win at Arminia Bielefeld on Sunday to climb to second in the Bundesliga, eight points behind champions Bayern Munich.Bielefeld, by far the better side in the first half, missed a chance to take the lead when David Kobylik struck a penalty against the bar in the 24th minute and Werder took advantage with a Frank Fahrenhorst header 18 minutes from time. Bayern, 3-1 winners at Borussia Moenchengladbach on Friday in the first league game back after the mid-season break, have 47 points from 18 matches. Werder have 39 points, with Hamburg SV third on 38 following their surprise 2-1 defeat at Nuremberg on Saturday. Schalke 04 consolidated fourth spot on Sunday by winning 2-0 at Kaiserslautern in their first game since former assistant coach Mirko Slomka stepped up to replace Ralf Rangnick. Last season's runners-up are 13 points behind Bayern and seven points ahead of fifth-placed Hertha Berlin. Werder, leading scorers in the Bundesliga, created only one clear chance in the first half when Tim Borowski's snap shot brought a good save from Mathias Hain in the ninth minute. Otherwise, Bielefeld were in charge and should have gone in front when Fahrenhorst's clumsy attempt to tackle Isaac Boakye led to a penalty. Boakye caused further problems a couple of minutes later when he raced on to a long ball forward only to slip his shot a metre wide. Werder's goal came thanks to the quick reactions of Fahrenhorst, who leapt to head past the stranded Hain after a Johan Micoud free kick had rebounded off the corner of post and bar. 'It was a lucky win,' Werder's sporting director Klaus Allofs told reporters. 'We weren't very clever in our play but we took our chance.'