Seanan Clucas had the first sight of goal for Glentoran on 10 minutes but could not steer his header on target off good work by Rory Donnelly.
Clucas tested home goalkeeper Paul Harrison from distance as the Glens pushed in search of an early boost following the home leg’s 1-1 draw in Belfast.
Adrian Cieslewicz and Declan McManus each fired wide for TNS across the initial exchanges before Conor McMenamin came close to breaking the deadlock off a goalmouth scramble.
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TNS grabbed full control of the tie with goals in quick succession on 26 and 27 minutes.
A penalty by McManus left TNS with the upper hand before, moments later, Leo Smith left the hosts home by 2-0.
The Glens survived conceding a third courtesy of the upright on the half-hour mark.
Donnelly’s header in response was saved by Harrison before Dayle Coleing was on hand to keep the deficit at 2-0.
Only the outstretched glove by Harrison stopped Robbie McDaid from closing the gap by capping McMenamin’s approach play with a Glentoran goal.
McDaid then attempted to turn provider for Clucas but the effort cleared the target.
Second-half pressure by the Glens featured a command of possession but TNS proved resolute.
Coleing had to be alert to cut out the threat from TNS on the break before pressure by the visitors led to Harrison scrambling the ball out for a corner-kick.
Glentoran battled for a way back into the tie but TNS managed to survive - with substitute Andrew Mitchell heading goalwards.
Injury-time attempts by McDaid and substitute Jamie McDonagh finished in frustration as TNS secured success.
THE NEW SAINTS: Harrison, Marriott, Astles, K.Davies (Ebbe, 76), D.Davies, Smith, Routledge, Clark, Cieslewicz, J.Williams (Robles, 68), McManus (Rees, 87).
Subs (not used): Roberts, Canavan, Daykin, T.Williams, Cornish.
GLENTORAN: Coleing, Kane, McClean, McCullough, Marron (Smith, 67), Marshall, Clucas (Mitchell, 56), Bigirimana (Cushnie, 81), McDaid, McMenamin, Donnelly (McDonagh, 67).
Subs (not used): Glendinning, Wightman, Stewart, Morris.
Referee: Ivar Orri Kristjansson.
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