Matt Kirby opened the scoring with a penalty for Clonakilty but Jeff Hitchmough had the sides tied 3-3 at the half time whistle.
Paddy Ryan scored a try which Kirby converted to make it 10-3 to the visitors, but Midleton hit back with a try from Gary McArdle and a second Hitchmough penalty to lead by a point.
Kirby was Clonakilty's hero kicking two penalties that still leaves them at the foot of the table but now just five points behind Instonians.
Old Crescent suffered a narrow home defeat to Greystones 19-14. Graham O'Keeffe scored a try for Crescent, Shane Mullally kicked two penalties and Tom Cregan one.
Thomond went down to an 18-8 away defeat to high flying Seapoint at Kilbogget Park.
Cashel go into the New Year on top of Division 2B after their 21-3 home win over neighbours Nenagh Ormond. Darragh O'Brien and Kevin Quinlan were try scorers for Cashel and O'Brien kicked three penalties and a convert. Donal Fogarty replied with a penalty for Nenagh.
Highfield travelled to Drogheda and shared the spoils with Boyne 19-19.
Sunday's Well slipped further down the table after their 24-9 away defeat by NUMI Barnhall. Shane O'Riordan kicked three first half penalties for the 'Well.
Ulster Bank League Division 2A: City of Derry 35, Instonians 14;
Corinthians , Bective Rangers ; late result
Dublin University 6, D.L.S.P. 3;
Malone 17, Queens University 15;
Midleton 11, Clonakilty 16;
Old Crescent 14, Greystones 19;
Old Wesley 12, Terenure College 32;
Seapoint 18, Thomond 8;
Division 2B: Banbridge 53, Ards 5;
Boyne 19, Highfield 19;
Cashel 21, Nenagh Ormond 3;
Navan 22, City of Armagh 12;
NUIM Barnhall 24, Sunday's Well 9;
Sligo 18, Rainey Old Boys 20;