The six-times world champion, at 39 the oldest competitor in the field, toiled for four hours 40 minutes before earning a last-eight meeting with Peter Ebdon.
After accounting for the first frame with a 97-break and moving 2-0 ahead, David trailed 4-3 as McManus threatened to take control by compiling a run of 90 in the seventh. But it was to be the Scot's last success of a dour contest as Davis kept things tight and won the next three frames to advance.
Davis, who has not added to his career-total of 70 titles since the Regal Welsh Open of January 1995, was "delighted" with both his fighting performance and the result. "Alan is easily the best player I've beaten in a tournament all season," he said.
Stephen Hendry enhanced his phenomenal record at the Masters by beating Brian Morgan 6-1 to set up a quarter-final against Ronnie O'Sullivan. But the Scot, victorious in 29 of 31 matches since making his Masters debut in 1989, was disappointed after failing to secure a maximum 147 break in the final frame when kissing the brown in trying to line up the 11th black.Reuse content