Prolific Constable took his Oxford goal haul to 91 after diverting right-back Damien Batt's angled drive past Plymouth goalkeeper Jake Cole to help his side record just their second win since New Year`s Day.
The Oxford target man could easily have doubled his tally but opted to pass when put through on goal by Sean Rigg's header in the 34th minute.
Argyle left-back Onismor Bhasera cut out Constable's pass, intended for attacking team-mates Josh Parker and Tom Craddock, as the U`s broke three-on-one.
Plymouth's on-loan Crystal Palace forward Jason Banton forced former Argyle keeper Luke McCormick to save low down to his left in first-half stoppage time.
And Cole then made a brilliant one-on-one stop to deny Oxford`s top scorer Tom Craddock in the 53rd minute following a poor back pass from Plymouth right-back Durrell Berry.
Seconds later, down the opposite flank, Constable's shot spun off the foot of the post.
Oxford skipper Jake Wright was forced to head Reuben Reid's goal-bound side-foot volley off the line following a 63rd minute free-kick as his held on for a vital win.
