'The Hammer' had been fortunate reach the last 16, having recorded a three-dart average of just 75.05 during his first-round win over John Part, who missed 18 match darts.
However, the Stoke-on-Trent thrower was able to put that horror show behind him, as he averaged 90.73 to defeat Dolan 9-3.
Dolan missed three darts at double 14 in the opening leg, allowing Hamilton to pinch a break of throw by checking out 90 on double five.
The heavy-scoring Irishman's double-trouble continued in the following leg, as he wasted eight more attempts at the outer ring before being punished by Hamilton's double top.
At the 13th time of asking, the 2011 World Grand Prix runner-up eventually got a leg under his belt, as double four came to his rescue.
After the next two legs had gone comfortably with throw, Dolan came within the width of a wire of completing a 108 finish for a much-needed break.
Hamilton made his opponent pay for that narrow miss by hitting double five for the third time in the match.