World number one Trump beat Australian Neil Robertson 6-3 in their quarter-final on Thursday
Trump took a 3-0 lead, making a break of 100 in the third frame for his 997th career century, before Robertson pegged him back to 4-3.
But in the end Bristol-born star survived the fightback as he won the next two frames to seal his place in the last four.
His compatriot Murphy had it easier going with a 6-2 victory over China’s Xiao Guodong, albeit making only one half-century break – a 61 in the eighth frame.