Stockport’s victory, combined with Wrexham’s draw at Boreham Wood, means Challinor’s men can win the title when the two teams clash at the Racecourse Ground on Sunday.
The Hatters won 1-0 at the Technique Stadium thanks to Paddy Madden’s first-half penalty.
The decision to award the spot-kick for handball against Calvin Miller was debatable and it was initially given as a free-kick outside the area.
Town came close to equalising three times after the break, twice through Jamie Grimes and then Jeff King.
“In the second-half we had to roll our sleeves up because these are a good team,” Challinor said.
"They have lost big players (to injury).
"This was a big win because this is a tough place to come.
"We have had to defend, I wouldn’t say ride our luck, but Ben (Hinchliffe) has had to make saves which you would hope he would do.
"If we have had a little bit of luck I am not bothered. I would not say that lots of things have gone our way in the last three or four weeks...today maybe it has.”
Stockport are now three points clear of Wrexham, who conceded a late equaliser at Boreham Wood.
It means the champagne could be popping for the Edgeley Park club this coming weekend.
"We knew that if we came here today and won that we would have the opportunity to go to Wrexham to win the league on Sunday and that was our sole focus,” Challinor added. “We have done that, we have given ourselves a chance.
"I believe in us that we are good enough to get out of this league but there is no good me believing it if they don’t believe it, they have got to back themselves individually.”