The wet conditions dictated the pattern of play at Magherafelt where all the points were scored in the first half.
Rainey reached the third round following a comfortable 22-3 win over BRA while their opponents were seeded in the top eight and were therefore expected to advance.
It was Rainey that took the lead following a well constructed try after 10 minutes. It came when winger Andrew Nicholl showed his pace to finish well after running past two defenders in the process.
Unfortunately for Rainey they conceded too many penalties and the visitors had a very competent kicker in Patrick Wright who was successful with two to make it 6-5.
The second period was a dull affair between two physically strong packs so there was little open rugby.
It was one of those typical cup ties were the next team to score would win and both came close as the pitch deteriorated.
By the end both squads had given their all and Down High had squeezed through.
Down High's coach John Gunson knew it was going to be difficult from the start.
“It was that sort of a day and I knew it would be closely contested with few tries. It turned out there was only one and it came from Rainey but Patrick Wright did us proud with those two penalties.
“We defended well when we had to but there were times when we failed to make full use of hard earned possession.
“We had to stand up to the pressure and I thought our Ulster under-18 squad member and No 8 Thomas Donnan was outstanding.
“He put in some strong tackles and controlled the line-out while Joseph Bingham at full-back defended stoutly, kicked well and was steadfast under the high ball. Out-half Ross Carlisle also performed well but I was especially pleased with the efforts of the pack.
“Rainey had a few formidable forwards and we did to keep them Under control.
“The game could have gone either way.
“Finally I would like to say that we have been improving in recent years and this is the first time we have reached the quarter-finals.
“The boys have put in a tremendous amount of work and the skills of our other coach Charlie Knox has made a big difference.”
Rainey coach Chris Campbell thought it was a typical Cup game
“Overall I thought we did well against a seeded team,” he said.
“We attacked and attacked towards the close but full credit to them as we just couldn't breach their defence and their discipline never wavered.
“Our full-back Mark Rooney put in a few strong tackles and his clearance kicks kept relieving the pressure. Back row forward Calvin Smith also made his presence felt in defence and out-half Kieran Lynch kicked accurately and intelligently.”
Down High now face a daunting task against Sullivan Upper.
At least they have home advantage but may need that asset when facing the Willie Anderson coached Holywood side.