In the 1913 season, Kilner scored 1,586 runs at an average of 34.47, which remained his highest seasonal aggregate of runs and placed him third in the Yorkshire batting averages. He also took 18 wickets at 25.22. At the end of May and beginning of June, Kilner took part in century partnerships in four consecutive matches, culminating in his maiden first-class century against Leicestershire. During his innings of 104, he hit 18 fours and shared a partnership of 184 in under two hours with his close friend Major Booth, rescuing Yorkshire from 58 for five and taking the score to 300. Throughout the season, he played several valuable innings when Yorkshire were under pressure. His batting was always adventurous and attacking although he often made uncertain starts to his innings and showed impatience. The strength and variety of the Yorkshire bowling attack meant his left-arm spin was not often required. Even so, Yorkshire dropped to second in the Championship.