St Helens, under the stewardship of new boss Paul Rowley, scored a total of 17 tries in a very professional display.
They put 50 points on before the half-time hooter as half-back Tristan Sailor took centre stage, scoring a first-half hat-trick, before Kyle Feldt and Jack Welsby completed the same feat after the break.
Jackson Hastings added 38 points with two tries and 15 successful kicks, meaning he ended the match just two points shy of a club record of 40 points in one match set by Paul Loughlin 40 years ago.
Two tries from full-back Cai Taylor-Wray and four kicks from Marc Sneyd helped Warrington to a routine win against Sheffield Eagles.
Wolves led by 10 points at the break but stepped up a gear in the second period with tries from Albert Hopoate and substitute Tommy Rhodes sealing the win.
Huddersfield Giants also sidestepped a potential upset with a convincing victory at Championship club Hunslet.
New Giants signing Chris Patolo scored inside four minutes on his debut for the club as Giants ran in 10 tries in total as Tui Lolohea grabbed two.
Four more Super League sides are in round three action on Saturday, including Leeds at Widnes and Leigh at Crusaders, before the fourth round draw on Monday evening.