The Broomfield men led 10-3 at the break but a sluggish beginning to the second period cost them two tries in the space of three minutes and all their momentum, a converted score in added time at the end finally sealing their fate.
But ex-Wharfedale points machine Davies, still on the mend from a broken leg sustained in the opening league game of the season, took some encouragement from the opening 40 minutes.
"I though we played well in the first half. They looked a good side but we defended soundly and showed enterprise," he said.
Crocs, still lacking several key men, were forced onto the back foot from the off and looked as though they might be overwhelmed by a side beaten only once in seven previous league outings this season.
But Durham discovered that trying to batter your way over the Crocs try line is often not easy and the home side appeared to have weathered the storm when they were awarded a penalty for crossing, only for referee Neal Gaskell to change his mind and award one to the visitors.
Winger James Walker's kick made it 0-3 but home scrum half Joel Hinchliffe levelled matters from Crocs' first incursion into visiting territory on 15 minutes.
Davies's men hit the front three minutes later when winger James Wainwright, who specialises in interceptions, picked off a Durham pass 10 metres inside his own half and scored with a diagonal run across the field to the corner.
Hinchliffe landed a fine conversion but missed a fairly straightforward penalty eight minutes before the break after Crocs had produced some exhilarating open rugby with outside centre Ryan Hammond and fullback Chris Seymour to the fore.
Durham, who had failed to capitalise on a couple of good breaks in the first period, swept in front on the back of poor kicks from home half-backs Chris Duffy and Hinchliffe.
Yorkshire referee Gaskell certainly couldn't be accused of being partisan after awarding a mystery penalty try to the hard-pressing visitors on 44 minutes and Durham No 8 Howard Johnson took advantage of a fortuitous bounce to notch his side's second try soon after. Left-footed kicker Walker added both goals to give Durham a 17-10 lead.
Johnson's try stemmed from poor quality Crocs lineout ball on half-way and the home men's failings in this area during the second half hindered their chances of getting back into the contest.
Hinchliffe, replacement Jack Hammond and Duffy all earned good field positions with excellent play but Crocs were unable to cash in and Durham responded through some excellent tactical kicks from stand off Richard Knowles to the bottom touchline.
The visitors finally clinched a deserved victory when replacement Mark McCreedy plunged over from a maul after a Walker penalty had come back off an upright.