Thomas O'Ware's second-half header proved enough as Morton extended their undefeated run in all competitions to three games with a narrow 1-0 victory over bottom side Alloa in the Scottish Championship.The visitors started brightest and came close to scoring an opener through Stefan McCluskey, Ross Forbes, Denny Johnstone and Bobby Barr, while visiting goalkeeper Grant Adam kept out efforts from Alloa duo Michael Chopra and Mark Williams at the other end.Despite Morton's first-half pressure, the score remained goalless at the break and it took until the 72nd minute before they broke the deadlock.Defender O'Ware was the man on target with his first goal of the season as he headed home Ricki Lamie's cross to clinch all three points.