A foul on Deuchar led to Gretna's opener with Derek Townsley squeezing in a far post header from Gavin Skelton's free-kick.
And Deuchar had a hand in the second by nodding down Ryan Baldacchino's pin-point cross for James Grady to fire in a volley after David Bingham had split the defence.
Deuchar should have made it three in the 26th minute when Ryan McGuffie sent him through one-on-one with the keeper but he dragged his shot across goal.
The miss seemed to galvanise the visitors and Gretna had some worrying moments as Raith rallied.
Todd Lumsden headed just wide from a Scott Crabbe corner on the half hour and a mix-up between Mark Birch and Alan Main almost let in Laurie Ellis.
When Steve Tosh lost possession in midfield, William Lyle raced down the flank to cross for Ellis to reduce the deficit with a powerful downward header in the 34th minute.
Gretna restored their two-goal cushion just before the break. Baldacchino skipped past two markers and Deuchar swept his cross past Alistair Brown with the help of a deflection.
Things got worse for Raith when they were reduced to 10 men after Crabbe saw red for a rash two-footed tackle on McGuffie.
Tosh added a fourth Gretna goal when the visitors failed to clear a Skelton cross and he finished crisply from 12 yards.
Grady grabbed his second goal of the game with a close-range strike that completed the scoring.