Playing his first match for Kent, Khaled marked his county debut with three wickets, while Hasan continued his excellent form by claiming four for 30.
The day began dramatically for Kent as Hasan struck with the first two balls of the innings. He removed Harry Came and Matthew Montgomery for ducks to leave Derbyshire reeling at 0 for 2.
Khaled soon joined the action, trapping Muhammed Naeem leg before for 12 before dismissing captain Wayne Madsen for 29.
Hasan returned to remove Brooke Guest for 11, while Khaled added Jack Morley's wicket to complete an impressive three-wicket haul on debut.
Despite the early damage, Martin Andersson led Derbyshire's recovery with an unbeaten 129. Luis Reece contributed 32, while Brett Randell added 29 as the hosts eventually reached 300.
Hasan finished with outstanding figures of 4 for 30 from 15.5 overs, while Khaled took 3 for 73 from 18 overs. Bertie Foreman claimed two wickets.
Kent's reply began cautiously, with Ben Compton falling for four early on. At stumps, Kent were 11 for 1 after six overs, still trailing Derbyshire by 289 runs.
Hasan's four-wicket haul came after his seven-wicket match-winning performance against Worcestershire, while Khaled made an immediate impression in his first County Championship appearance for Kent.
