The caretaker boss has been given some fans' backing to replace Dave Hockaday on a permanent basis.
Stephen Warnock's first-half winner was enough to secure three vital points, despite a dominant performance from the visitors. It was Redfearn's first game of the season - but not his first in charge at Elland Road.
Indeed, this is Redfearn's third spell in caretaker charge at Leeds and speculation has linked him with the job on a permanent basis.
Intriguingly, the 49-year-old has not ruled himself out of the running for the post.
"I love coaching and working with players," he told reporters after the game.
"The most important thing is that the appointment is right for the football club. I will have a chat with the president and see what he is thinking.
"It is his decision but the club needs a settled set of circumstances."
That should please several Leeds fans, as many have welcomed the speculation in the wake of Leeds' Bolton win.
Supporters took to Twitter after the game to express their view that the Yorkshire club should give Redfearn a chance. After all, he'd probably make a better manager than Dave Hockaday.
Next up will be two away games at Birmingham and then Bournemouth. First, though, here are a selection of the best reactions to Leeds' win...
I think we should give Neil Redfearn a go at being manager. #lufc— Jacob Newbould (@JacobNewbould) August 30, 2014
Just got home from Leeds. Much better today. Can do a lot worse than giving Neil Redfearn the job full time. #lufc— Jamie Wilby (@JamieWilby1) August 30, 2014
Not a bad word can be said about Neil redfearn, he truly is leeds and has done an outstanding job on a number of occasions— Tom Parton (@tparton95) August 30, 2014
@mfeee7 seriously , give Neil Redfearn the job, please tell the President its what the fans want— DB (@dale_brown_) August 30, 2014
Sign up Neil Redfearn— Arve Tokvam (@atokvam) August 30, 2014
I've said it a million times. Neil Redfearn should be manager. Said it after Grayson, Warnock and when McDermott got "sacked".— Shaun Eccles (@Thecharmlessman) August 30, 2014