Rory McIlroy made five straight birdies down the stretch to overtake Justin Rose and win the Dubai World Championship on Sunday, ending a historic year in which the 23-year-old Northern Irishman won the PGA Championship and the European and PGA Tour money titles. The top-ranked McIlroy recovered from early putting woes to finish at 6-under-par 66 for a 23-under 265 total at the season-ending tournament. Rose surged down the stretch after shooting a course-record 62 that included an eagle and eight birdies. ‘‘I just wanted to finish the season the way I thought I deserved to finish the season,’’ McIlroy said after holing a birdie on 18. Second-ranked Luke Donald (71) was tied for third with Charl Schwartzel (68). Louis Oosthuizen (69) was another shot back in fifth.