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The Reds have lifted the trophy in each of the last three seasons and will aim to repeat the feat on 13 February.
Donnelly's backpost volley from Stephen Garrett's cross was enough to win the tie for the holders, who now face Ards.
Warrenpoint players Mark Clarke and Liam Bagnall were sent-off, while manager Barry Gray was also dismissed.
The game was played in horrendous conditions but the Reds created few chances with the wind in their favour in the opening period.
Tomas Cosgrove flashed a header wide of the post while Stephen Garrett mis-kicked with the goal gaping.
The hosts suffered a setback in the 77th minute when Clarke received a second yellow card for a challenge on James Knowles and then Donnelly ensured a 19th successive win in the competition for the Reds with his ninth goal of the season.
Donnelly had a chance to extend his side's lead, before Gray was sent to the sidelines for dissent and Bagnall was shown a second yellow late in the game.
Jay Donnelly's winning goal two minutes into the first period of extra-time secured Cliftonville's passage into a fourth consecutive League Cup decider.