Mark Selby held off a fine late fightback from Ryan Day, who had earlier made a 147 break and then a 16-red total clearance, to book his place in the semi-finals of the Duelbits Tour Championship in Hull.Having lost the opening two frames at the Bonus Arena, Welshman Day produced a perfect response with a third career maximum after potting the last two reds from difficult positions to put himself in contention for the £10,000 highest-break prize.However, it was world number two Selby who finished the afternoon session with a 6-2 lead, which included a 132 clearance in the seventh frame, as he looked to secure a semi-final against Shaun Murphy.Selby, winner of last week's WST Classic on home soil in Leicester, further stretched his advantage with a run of 131 at the start of the evening, before Day pulled a couple of frames back to trail 8-4 heading into the mid-session interval.The Welshman reduced the deficit again with a break of 75 but spurned another winning position in the next when he screwed back off a pink into the middle pocket, allowing Selby back to clinch the 14th frame and move within sight of the finish.Day, the 2022 British Open champion, made a superb 16-red clearance of 139 on his way to closing back to within two before Selby – who can regain the world number one spot by reaching the final – made a break of 77 as he wrapped up a hard-earned 10-7 victory.