Florian Kamberi, Scott Allan and Fraser Murray scored the goals on a straightforward evening for Paul Heckingbottom's side.
Hibs can guarantee progression to the second round with victory in Friday's match at Elgin City.
With Josh Vela making his debut in midfield among six changes made by head coach Heckingbottom, the hosts broke the deadlock in the third minute.
Kamberi raced on to Allan's ball inside the area and beat Arbroath goalkeeper Darren Jamieson from a tight angle.
With the exception of a Bobby Linn free-kick that Hibs goalkeeper Chris Maxwell got behind, it was the hosts who were causing all the problems.
Red Lichties goalkeeper Jamieson was well positioned to get behind a Stevie Mallan drive and Martin Boyle half volley, both efforts coming from outside the area, while Adam Jackson headed just over from Joe Newell's deep corner.
The second goal finally came a minute before the break after Allan found the net from the penalty spot.
Referee Bobby Madden initially allowed play to continue when Boyle was taken out by Thomas O'Brien after crossing for Kamberi, who had struck an overhead kick just over.
Hibs continued to press after the break but Jackson had a header saved by Jamieson before Paul Hanlon nodded over when he should have scored.
However, the third finally arrived when Murray tucked away Daryl Horgan's cross at the front post.