Recalled Mustapha Bundu scored a 21st-minute winner, while home keeper Michael Cooper made a string of stops as Leicester piled on the pressure, but the hosts held on for maximum points.
Dewsnip said: "We are absolutely delighted. We are made up. We still have a target and that is to stay in this league.
"It's been the same since day one when we started in the Championship. It's been a great night for Plymouth Argyle.
"We still have three more games to play and more points to play for.
"The players stuck to the shape we wanted and I am delighted we stuck to the game plan.
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