After slipping to 34-2 early on the final day chasing 329 for victory, Rob Key (67) and skipper Sam Northeast (76) took Kent to 139-3 with a stand of 105.
Ben Harmison's breezy knock of 50 took the visitors to 231-4 before he was dismissed on the stroke of tea.
Rain then prevented any further action with Kent needing 98 more runs and Derbyshire five more wickets to win.
On a fluctuating last day, Derbyshire seized the early initiative after Ben Cotton bowled Daniel Bell-Drummond for 19 and England hopeful Mark Footit (2-64) had Joe Denly caught behind by teenage wicketkeeper Harvey Hosein for a single inside their first three overs.
Key and Northeast's century partnership led a Kent recovery before Tony Palladino trapped Key lbw. Harmison kept the momentum up until Hosein and Footit combined again to remove Northeast, 24 runs short of his first century of the season.
The match was back in the balance when Harmison was dismissed immediately after reaching the 15th first-class half-century of his career off 63 balls, including eight fours.
The home side reached tea on 231-5, but persistent drizzle meant they players never returned to the field with the match abandoned as a draw at 17:30 BST.
Kent remain second-bottom of Division Two with Derbyshire one place and 12 points above them.
Derbyshire and Kent had to settle for a draw after rain ended both sides' hopes of winning their finely-poised match.