First-half goals from Darren Byfield and Tom Brighton were enough to earn Millwall their fifth win in six matches against struggling Cheltenham.
Byfield scored the opener by outjumping Shane Duff to power home Brighton's cross for his 13th goal of the season.
Brighton then made it two nine minutes later when he broke the offside trap before slipping the ball under the advancing Higgs.
Steven Gillespie came close late in the game for Cheltenham.
Millwall: Pidgeley, Craig, Shaw, Robinson, Senda, Byfield, Elliott, Ardley (Dunne 75), Brammer (Hackett 86), Brighton (Zebroski 76), Harris.
Subs Not Used: Day, Hubertz.
Goals: Byfield 33, Brighton 42.
Cheltenham: Higgs, Gill (Bird 50), Duff, Lowe, Townsend, Yao (Gillespie 47), Finnigan, Connolly, Armstrong, Odejayi, Spencer (Connor 76).
Subs Not Used: Caines, Scott Brown.
Ref: A Penn (W Midlands).