On a bizarre afternoon the game was switched from the waterlogged first-team pitch to one out the back, but the late change seemed to inspire the visitors.
They began strongly, Oli Rhoads opening the scoring with a brilliant 40-metre finish down the left after being set free by Zach Clow.
Mike Cooke landed a fine conversion, but Lions responded swiftly, hammering away at the line with a series of pick-and-goes before Bronson Mellowes eventually barged over.
Rams seize control
The scores were level when Luke Bouchier slotted the extras, yet Rams regained the lead as captain Max Hayman rode a maul over for 12-7.
But the visitors were temporarily reduced to 14 men after Aaron Tull infringed at a breakdown near his own line, and Leicester elected to take a simple three points via the boot of Bouchier.
Rams, however, struck back with Hayman doubling up from the set-piece, Cooke on target for a nine-point advantage.
The away side came under the cosh at the end of the opening 40 minutes, but in a key moment, they withheld immense and sustained pressure to hold out.
After a short half-time with neither side wanting to trek back to the changing rooms, Rams had the benefit of the slope in the second period and came firing out the blocks as Hayman completed his hat-trick from another maul.
Cooke slotted another cracker, and Lions were then reduced to 13 with Jake Sterland and Mellowes yellow-carded in quick succession, the latter also precipitating a penalty try after illegally stopping another ferocious maul.
Duo make debuts before Lions bag consolations
Teenage duo Harry Bicknell and Paddy Jackson were introduced for debuts off the bench – Hayman briefly switching to No. 8 as he became just the second Rams player to score four in a National One fixture.
On this occasion it was Ben Atkins who made the initial break, the visitors stopped just short before the captain hoovered up the ball to dive over from a metre out.
Leicester refused to yield, however, and grabbed a second try after benefitting from what appeared to be obstruction in midfield, a grubber kick grounded on the right by Sterland.
And they had the final word with a maul of their own, Joe Plummer getting the ball down, Bouchier on target twice more with the latter the last play of the game.
Rams have a weekend off before hosting table-toppers Rotherham Titans for the Christmas fixture on Saturday, December 6.
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