Glentoran forward Michael Halliday scored the opener
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The Glens replaced Armagh at the top of Group One in the CIS Cup after this hard-fought victory at Holm Park.
Glentoran striker Michael Halliday opened the scoring with a six-yard header on 30 minutes.
Derek Delaney's headed in an Armagh equaliser a minute after the break but Jody Tolan restored the Glens' lead with a deflected 49th minute shot.
City had chances to draw level again with Barry Meehan wasting the best opening by striking the crossbar.