Hawkins rattled off the first frame of their second session with a break of 68 and then used his superior match play experience to take the next three to win the match before the mid-session interval.
Lisowski, a potter and break-builder of some quality, let the match slip away from him with some poor safety shots; one example of which was inexplicably rolling the cue ball into the pink during the 11th frame when presented with a one-cushion escape and the full 15 reds on the table.
Hawkins won the next three frames 61-31, 75-36 and 71-21 to secure a spot in the last-16.
Hawkins will face the winner of Mark Selby and Matthew Selt, who play on Tuesday.
Lisowski won the final frame of his opening session at the Crucible to stay in touch with Hawkins at 6-3 in Sheffield.
Lisowski, making his debut at the Crucible, took the first frame courtesy of a break of 82 in reply to Hawkins's 53 but the world number 14 responded magnificently to go to the interval with a 3-1 advantages.
He claimed the second frame 60-16 and then squeezed past Lisowski courtesy of a 59 break in a closely fought 69-61 third frame.
A half-century break in the fourth ensured that Hawkins went to the interval with a two-frame advantage but Lisowski made a 100 break in response to take the first frame after the mid-session interval.
Hawkins then opened up a four-frame advantage with breaks of 97,100 and 66 but Lisowski, who has battled back from Hodgkin's lymphoma cancer and is still only 21, ground out a turgid final frame 26-49 to leave the match finely poised at 6-3.