Dewsbury-Hall scored his first Premier League goal
The Foxes started slowly at the King Power Stadium but Dewsbury-Hall carved Palace open with a superb ball for Ademola Lookman to fire home, before whipping his own finish high into the net six minutes later.
"It means so much," he said of his first Premier League goal. "It's a dream come true to score in the Premier League. I have dreamt it since I was a little boy. I have come close but I am so happy today."
The 23-year-old's moments of quality proved telling in a fixture both sides could have been forgiven for looking past given their mid-table status and with key cup fixtures in the coming week.
Palace - who missed early chances through Wilfried Zaha, Jean-Philippe Mateta and Joachim Andersen - refused to give in after the break and Youri Tielemans' foul on Jordan Ayew in the penalty area offered them a route back into the match.
Zaha saw his penalty saved and when VAR pointed to encroachment in the area by home defender Caglar Soyuncu, his retaken penalty was also palmed away by Kasper Schmeichel, only for the Ivory Coast international to head in the rebound.
It prompted a spirited 10 minutes from Palace - who went close through a Jeffrey Schlupp flick - but their seven-game unbeaten run ends. Leicester now have four wins and a draw from their past six league games - form that lifts them to ninth in the table, one place above the beaten visitors.
A closely matched game - possession was 50-50, while Leicester managed just one more shot than their visitors - was arguably to be expected given two sides enjoying very similar fortunes.
Leicester did not pick up a league win for all of January and February but have found late-season form. Palace won just once over the same period and have themselves found momentum deep in the campaign.
Throw in the fact that Leicester face a key Europa Conference League second leg against PSV Eindhoven on Wednesday while Palace have one eye on next Sunday's FA Cup semi-final against Chelsea and it would be easy to see why either side might have opted to preserve energy.
And Leicester's seven changes from their 0-0 first-leg draw with PSV appeared to cause a lack of cohesion that Palace might have exploited.
But the visitors were unable to take half-chances and Dewsbury-Hall made them pay by reversing a defence-splitting pass into Lookman's path for the opener before patiently creating shooting space of his own for a rifled second.
The 23-year-old was certainly not coasting. He ran further than anyone else on the pitch - clocking 11.3km - and hit a higher top speed than anyone in his sprints.
"Since he's broken into the team I felt throughout the season it was what we were missing," Leicester manager Brendan Rodgers said of Dewsbury-Hall.
"The team was missing intensity and pressure and he has brought that. He typifies everything we want to be. He has good industry, a cultured left foot and he's very honest."
Palace, who have not ended a top-flight campaign higher than 10th since finishing third 1990-91, will rue a period late in the first half when they slackened off and let the Foxes in.
Dewsbury-Hall's assist saw them opened too easily, while his goal owed much to a missed clearance by Marc Guehi in the build-up.
When they did rally, Zaha was integral to the improvement and his form will offer confidence for next week's semi-final.
After scoring, he fought admirably to conjure an equaliser, notably when teeing up Schlupp who saw his flick blocked by a sea of Leicester bodies.
-- Courtesy of BBC Sport