The veteran frontmen proved to be the difference between the sides in a game of few chances.
Hughes atoned for a poor first-half miss by striking twice in the second half after Byfield had fired the Latics in front.
Their goals kept John Sheridan's side in the hunt for promotion from League One.
Crewe worked hard in Dario Gradi's last home game in charge before he hands over to new boss Gudjon Thordarson, but created little in front of goal.
Full-back John Brayford came closest to scoring in the first half, but was denied by a good stop from Greg Fleming after he flicked on a cross from stand-in left-back Colin Daniel.
Mark Carrington's loose backpass let in Hughes clear on goal just before the half-hour mark, but the striker side-footed his finish woefully past the far post.
Byfield went close with two snapshots and an overhead kick tested home keeper Stuart Tomlinson.
But Oldham got on top after the break and Tomlinson held on to Chris Taylor's shot.
Crewe threatened when Eugen Bopp's curling cross almost found the head of Byron Moore at the far post, only for Reuben Hazell to make a vital clearing header.
And Byfield took advantage of a slip from Danny O'Donnell to fire the Latics in front in the 57th minute, beating Tomlinson at the near post.
Moore drove a low shot past the post as Crewe tried to respond, but they were two down in the 67th minute.
Hughes's predatory finishing did the trick as he took a pass from Keiron Lee and curled a side-footed finish just inside the far post.
The former West Brom striker, who has a habit of scoring at Gresty Road, then met substitute Lewis Alessandra's cross with a thumping header for his second and his side's third with six minutes left.