A 35th-minute strike by Asa Hall surprised the Shakers and it got worse when defender Ben Futcher went off with a hamstring injury.
But Bury battled back after the break to claim their fourth win in five games and stay in third place in the table - thanks to a 59th minute equaliser from Andy Bishop and Morrell's winner seven minutes later.
"We said all along that Andy came with a good CV," said Knill. "He's had a good career and we think he can have a longer career with us.
"You know there's quality there and it will come.
"Just before he started scoring he wasn't getting chances. Then he gets one, a pretty poor one against Aldershot, and now he's having loads of chances and looks brighter when the ball comes in the box."
Luton had threatened in the first half with Hall firing one wide and then having a goal denied by a fine reflex save from Mark Tyler.
Bury hit straight back, though, with Bishop having a shot cleared off the line and testing Conrad Logan with two long-range efforts while Morrell saw a superb strike come back off a post.
Luton took the lead when Tom Craddock's run was blocked by Paul Scott and the ball came out for Hall to score.
But Bury made a strong start to the second half and drew level when Bishop pounced to turn in Bennett's deflected cross.
The Shakers were rampant now and went in front as Bennett crossed for Morrell to score with a diving header.
"It was a great win, especially being 1-0 down and losing your centre- half," added Knill. "I thought we were excellent in the second half and were more than value for the win."
BURY: Tyler 7; Scott 7, Cresswell 8, Futcher 7 (Sodje 42, 7), Buchanan 6; Bennett 8, Dawson 7, Barry-Murphy 7, Jones 8; Bishop 8, Morrell 8 (Hurst 83), Subs: Baker, Haslam, Racchi.
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