Walters flashed a half-volley just wide 7 minutes later, while the linesman denied City any more clearcut chances in a half they clearly dominated.
Just before the hour mark, Walters went inches wide with a shot that had beaten Morris.
An awful backpass by Tom Newey almost put Ben Burgess through. He won the slide tackle with Morris, but Mark Peters raced in to make a crucial challenge as Burgess got to his feet.
Junior Lewis then looked to get his first Tigers goal by catching Morris out of position, but his effort from just inside the Orient half didn't have enough power on it and the 'keeper got back in time.
The visitors had a string of corners but City held on, before Danny Allsopp was introduced in the 66th minute, replacing Walters up front.
City added a second goal in the 78th minute. Jason Price worked the ball to Ian Ashbee on the right wing and his far post cross found Ben Burgess, who headed home his 15th of the season.
Yet another poor decision from the linesman saw captain Ian Ashbee booked for dissent. That's his 10th yellow card of the season, and he'll now be suspended for the games against Boston and Kidderminster.
Peters denied a goal with a Allsopp had a shot blocked before Ryan France wrapped up the win in stoppage time. Stuart Green's cross from the byline on the left found France at the back post who nodded in for 3-0.
City line-up (4-4-2): Myhill; Marshall, Joseph, Delaney, Thelwell; Price (France 86), Ashbee, Lewis, Elliott (Green 76); Walters (Allsopp 66), Burgess.
Un-used subs: Musselwhite, Hinds.