Cork got a dream start when Cummins headed home from close range after Mervue goalkeeper Ger Hanley had saved from Danny Murphy as the visitors pressed from the start.
Galway native Daryl Horgan almost made it 2-0 after 12 minutes but Hanley did well to deny him.
Cork’s failure to put away chances allowed the home side to recover but they rarely looked like grabbing an equalier.
Cummins struck for his second three minutes from the break when he stooped to head home a cross from Vincent Escude Candau.
But Mervue fought back after the restart when Cork’s Shane Duggan was sent off for a challenge on Alex Lee on the stroke of half-time.
Pat Hoban pulled a goal back from the penalty spot three minutes after the restart after Peter Dravins was fouled.
Mervue almost levelled after 65 minutes but Mark McNulty did well to save from Dravins.
McNulty had to go off after 70 minutes following a heavy challenge which earned James Casserley a yellow card for Mervue.
Horgan should have wrapped up the issue three minutes from the end of normal time when he rounded Hanley but Martin Conneely did well to get back and avert the danger.
Mervue tried gamely for a later equaliser but Cork held for a valuable win.
Hanley; O’Brien, Ludden, Conneely, Casserley (Keogh, 83); Mountney, Molloy, Lee (Nkololo, 55), Crehan; Hoban, Dravins (McEntee, 82).
McNulty (McCarthy, 70); Turner, Spillane, Murphy, Kavanagh; O’Brien (Sullivan, 82), Morrissey, Horgan, Duggan; Escude Candau, Cummins.