A strong mid-match performance, in which they scored all their points in the space of 34 minutes, helped them comfortably overcome an already-relegated York side.
Hartlepool Rovers, who lost 22-17 at champions West Hartepool, slipped into the drop zone and Crocs also moved above Carlisle, 26-18 home winners against Driffield, on points difference.
It all added up to a satisfactory outcome for Crocs player-coach Jonathan Davies after what must have ranked as one of the most difficult seasons in his lengthy career.
The ex-Wharfedale man broke a leg in the opening game at Carlisle and had to sit and suffer while his men slid down the table following a promising start.
Davies, by his own admission, is still far from fully fit but his influence at stand off on Saturday was the key factor as Crocs overcame their nerves and a tardy performance in the first quarter to save their bacon.
"The overwhelming emotion is relief - we're glad to get the threat of relegation out of the way," said Davies.
"We must look to strengthen the squad in the close season and in the long term we need to get a youth team back at the club."
The only downside for Davies was the dislocated elbow suffered by lock Mark Jowett in the opening 10 minutes, an injury which added to an uncomfortable start for the home men.
York played with more cohesion in the opening half hour and were good value for their 3-0 lead which came courtesy of fullback Neil McLure's straightforward 15th minute penalty for offside.
It might have been worse for Crocs, desperate tackling preventing flanker Oli Councell grounding the ball over the try line and McLure being narrowly off target with a second penalty attempt on 27 minutes.
A couple of intelligent grubber kicks to touch from Davies helped push York back into their own half and it was the player-coach's break on 30 minutes, well supported by back rower Adam Hinchliffe, which marked the turning point of the match and led to Crocs' first try.
Winger James Wainwright was held up over the line in the next passage of play but, from the resulting scrum, Crocs were awarded a penalty try when their march to the line was illegally stopped twice by the visitors. Davies converted for a 7-3 lead against the run of play.
The home forwards now had the bit between their teeth and although Crocs' outside backs still looked short of confidence, a Davies penalty just before the interval whistle was reward for a spell of intense pressure.
Turning round 10-3 up, Crocs launched a flowing attack through Gareth Ott, Jack Hammond and James Wainwright and although it didn't produce points, York centre Sam Arkle was yellow carded.
A blockbusting run from Stuart Hill, now playing in the second row, might have led to a try wide on the left but winger Ian Holmes was unable to cling on to the pass.
Eventually, however, the dam burst and the result was converted tries after 51 and 57 minutes. Hinchliffe cashed in when Crocs took a scrum against the head close to the visitors' line and then Chris Duffy sent in Hammond for an excellent try.
Davies added both conversions and a 64th minute penalty after some excellent approach play involving backs Jack Hammond, Wainwright and Neil Richardson.
York fullback McLure was yellow carded but when the home side's lineout king Chris Wood and Duffy suffered a similar fate, York made the most of their numerical advantage to notch a 79th minute try from prop Daz Rutherford wide on the left.