The Yorkshire side took an early lead and fought their way back in front with three minutes remaining, only to have victory snatched from their grasp.
Ionians drew first blood with No 8 Daniel Paul touching down in the 10th minute. The conversion was missed and Blackheath hit back with flanker Davidf Allen scoring and full-back Leo Fielding adding the conversion.
Home side flanker Laurence Cowen scored in the 27th minute and Isaac Green was this time on target with the kick which put them 12-7 ahead, but the scores were tied at the break after hooker Scott Wright barged his way over.
A penalty from Green pulled Ionians back in front at 15-12, only for a 60th-inute penalty try to be converted by Simon Whatling as Blackheath regained the lead at 19-15 with 20 minutes left.
Once again Hull Ionians hit back with Paul’s second try coming in the 77th minute to put them one point ahead at 20-19.
But hopes of a win proved premature as second-row Greg Gillanders touched down and Whatling converted to seal victory.
Wharfedale’s brave defence proved to no avail as they suffered a 55-12 defeat at Richmond.
On a cold breezy day, the pitch was in perfect condition for running rugby but both sides were initially riddled with ball-handling errors.
Wharfedale took the lead after retaining possession from a lineout. Several phases later and a tap penalty resulted in a well-worked try in the corner for Max Labasse but Harry Skelton failed to convert.
Jack Alcock touched down from a catch and drive and Rob Kirby’s boot put Richmond ahead only for the Greens to strike back.
Cameron Hudson made an excellent break and quick recycling of the ball saw Dan Tai score in the corner with Skelton adding the extras.
That was as good as it got for the visitors and Richmond led 22-12 at the break, Kirby kicking a penalty and converting one of the tries from Chris Davies, in his 150th game, and Callum Grant.
Richmond played with great pace and tempo after the break and soon scored converted tries through Will Warden and Rory Damant.
Wharfedale defended bravely but found it difficult to break out of their own half.
The pressure finally told and further tries from Rory Damant, Sam Stuart and Adam Gadsby, two converted by Kirby, took the final score to 55-12.