Midfielder Dewsbury-Hall – who is yet to make a Premier League start – replaced Boubakary Soumare on the south coast and helped the Foxes overcome a dismal opening period to secure a deserved 2-2 draw.
City, who trailed 2-1 at the break, were significantly better after the restart and squandered excellent chances for a winner through Harvey Barnes and Jamie Vardy following James Maddison’s superb leveller.
Leicester manager Rodgers was delighted with the impact of his half-time alteration, heaping praise on 23-year-old academy graduate Dewsbury-Hall, who spent last season on loan at Luton.
“I thought Kiernan was outstanding,” said Rodgers. “He wanted to prove a point, he was aggressive and he took on the burden of the game.
“He knows the position that we want him to play. He has good energy and good athleticism.
“I’ve said about him improving on the ball, but he can give us that bite in midfield and he was a catalyst for the second half.”
Southampton had the better of the opening 45 minutes and twice punished slack Leicester defending following corners.
Jan Bednarek poked Saints into an early lead and, after Jonny Evans equalised, Che Adams restored the advantage with a diving header.
Maddison’s fine effort just after the interval again drew the Foxes level before home goalkeeper Alex McCarthy produced an excellent fingertip save to deny Barnes and Vardy blazed over when clean through.
Defender Evans – who was on the scoresheet for the first time since equalising in a 1-1 draw in last season’s corresponding fixture – admits there were “some harsh words” in the changing room at half-time.
“Before the game, you are always coming here wanting three points – I think that’s our mindset,” the 33-year-old told Leicester’s website.
“It’s been our mindset for a couple of years now and we want to be at that level where we’re coming away dominating games and winning games.
“There were some harsh words at half-time and we knew that we had to respond.”
A point for Southampton followed a disappointing 2-1 loss at lowly Norwich and last weekend’s 4-0 thrashing at Liverpool.
Saints boss Ralph Hasenhuttl hailed keeper McCarthy for atoning for his poor performance at Carrow Road by keeping Leicester at bay.
“I must say Alex made fantastic saves to keep us in the game,” said Hasenhuttl.
“He saved us a point. Against Norwich he lost us a point, he knows this, that he didn’t do a good job there. But I must say he has played a good season.”