Jonny Howson grabbed the third immediately after half-time, and after Andy Barcham pulled one back for Gillingham after 50 minutes, Jermaine Beckford hit Leeds' fourth 11 minutes from time to set them up nicely for a Carling Cup clash with Liverpool in midweek.
Johnson headed his first from a corner floated into the six-yard box by Robert Snodgrass.
It could have been a different story if Barcham had taken a golden chance at the other end a minute earlier and Curtis Weston wasted another good opportunity against his former club just before half-time.
Former Northampton winger Johnson struck again for his fifth goal of the season in the 28th minute. Beckford released him on the left and Johnson rode Barry Fuller's challenge before beating goalkeeper Simon Royce at his near post.
Howson chested down Beckford's flicked header before shooting past Royce to make it three, Barcham struck from 10 yards when Leigh Bromby failed to clear Kevin Maher's free-kick, and Beckford followed up to score when Michael Doyle's shot hit Gillingham's crossbar to complete the scoring.