The goal arrived on 74 minutes when Boyce put the ball out of reach of City ‘keeper Tiernan Brooks at the Shed end.
Because of illness in the camp, Cork boss Richie Holland was forced to make four changes while the Candydtripes made three and had midfielder Sadou Diallo suspended.
The win guarantees Derry European football next season even though Ruaidhri Higgins’ side have a less than 50% win record all season.
Derry with one win in their last five games opted for a 4-2-3-1 formation, the same as the home team, and just about shaded this contest.
Cork needing seven points from three games to escape the play-offs made a bright start with top scorer, Ruairi Keating winning two headers in the air but he lacked support up top.
Ten minutes in and midfielder Ben Worman had a shot from outside the box deflected wide as the Rebels made the better start to what was their second last home game of the campaign.
Derry’s Jamie McGonigle, a doubt before kick-off, was on the bench.
On the restart, Michael Duffy rattled the post for Derry and Brooks saved well from Adam O’Reilly.
Derry should have made it 2-0 late on but front man, Danny Mullen dragged his low shot wide of the far post as Cork pressed for an equaliser that never materialised.
So victory cements European football for the Candystripes while Cork are now all but guaranteed a play-off berth with Waterford or Cobh Ramblers their likely opponents on November 10.
Cork City: Brooks; Custovic (Walker 69), Coleman (Owolabi 84), Hakkinen, Honohan; Bolger, Kravchuk; Bargary (Kabia 69), Coffey (Dijksteel 61), Worman (Murphy 69); Keating.
Derry City: Maher; Boyce, Connolly, McJannet (capt), Doherty; Dummigan, O’Reilly (Mullen 72); Kavanagh (McEneff 72), Patching, McMullen (P. McEleney 72); Duffy (Coll 90).
Referee: Damien McGraith (Mayo)Tags: