Gijon started the match strongly, with Halilovic striking over from the edge of the area in the 13th minute.
Jony thought that he had given Gijon the lead a minute later but his goal was ruled out for offside.
That save proved to be important as Barcelona loanee Halilovic opened the scoring on the half-hour mark when his shot nestled inside the left post for what proved to be the winning goal.
Halilovic received the ball inside the penalty area in the 81st minute but his first-time shot struck the crossbar.
The result sees Gijon rise to 12th in the La Liga table.