The 22-year-old clocked 57.75 seconds as fellow Briton Ross Murdoch also made it through as sixth-fastest qualifier.
Peaty, who will defend his 50m and 100m titles, told BBC Sport: “56 seconds is achievable whether it’s tomorrow or in three years. I’ll definitely get it.”
Guy, an Olympic silver medallist in men’s 4x200m freestyle relay, will race in the preliminary rounds of his favoured event – the 200m freestyle – on Monday.
“Based off this morning I thought I’d go faster than that, but tonight it just felt a bit tougher,” he told BBC Sport.
“The effort was there but the time wasn’t. But it’s the 200m tomorrow and that’s a better event for me. I know I’m in good shape so I just need to do it in the pool.”
Team GB Olympic silver medallist Siobhan-Marie O’Connor qualified fourth-quickest for Monday’s 200m individual medley final but team-mate Hannah Miley missed out.
Olympic finallist Ben Proud will be expected to challenge for a medal on Monday when he returns for the 50m butterfly final after impressing in Sunday’s opening-night semi-finals.
American Katie Ledecky set a new World Championships record of three minutes 56:06 seconds in the women’s 400m freestyle final to take the gold medal as China’s Sun Yang won the men’s event.