They were denied a quarter-final spot by a determined display from Stanley View Lane Park, skipped by John Leeman.
A four to Harrington on the 11th end seemed to tip the scales in the Oxford trio's favour, but five shots to Leeman on the 13th and a three on the 16th left Summertown 19-12 adrift.
Harrington, who twice sent the jack out of bounds, managed a treble on the 17th to narrow the gap to 19-15. But Leeman, whose middle man Chris Palmer was a tower of strength, notched up a double on the 18th to win 21-15.
The morning was fruitful for Suffolk's Roy Cutts, whose business commitments ruled him out of the opening rounds on Thursday.
Replacing Adrian Wyatt, who had stood in successfully for him, Cutts won through after a nervous start.
Greenhill (Weymouth) notched up another good victory over Long Eaton.Reuse content