Only leaders Richmond had managed to beat Mowden Park in the last four months prior to Saturday.
But Albion return home from the 750-mile round trip with four valuable points thanks to a hat-trick of tries by number eight Herbie Stupple and three conversions and a penalty from fellow Cornishman Matt Shepherd.
However, director of rugby Dawe was keen to point out what a squad effort the victory in the North East was.
Albion, already without influential centre Marc Koteczky due to suspension and injured fly-half Elliot Bale, lost experienced lock Dan Collier before the match and then Ethan Ford and Ollie Dawe during the game with injuries.
“It was a real squad effort, not a team or one individual,” said Dawe.
“This team really do believe in one another and at half-time they were calm and knew the job they had to do.”
He added: “This was a hard-earned victory on the road. The game could have gone either way, but Matt Shepherd’s final conversion was the icing on the cake as they would have had to score twice to win the game. The conversions were key as well as the scrum.”
Albion destroyed Darlington at the scrum and that proved the platform for the victory.
“Our scrum is something we are continuing to work on and long may it be a force,” said Dawe.
Darlington’s home record has been impressive, but so has Albion’s away record. Dawe’s side are unbeaten on their travels since November, claiming consecutive victories at Wharfedale, Hartpury College, Rosslyn Park, Fylde, Esher, Cinderford and now Darlington.
“It was quite an intimating arena, with the home supporters making a lot of noise and it echoes around, which puts a lot of pressure on the referee,” said Dawe about Saturday’s venue.
“We came a good second in the penalty count first half and we found it very hard to get any rhythm.
“But the guys kept at it, kept their belief and kept their structure. I thought our kick and power game won us the match.
“But give a lot of credit to Darlington. Their running game is strong and their power game. Their discipline seemed strong, although we felt they were going off their feet at the tackle quite easily.”
Albion are without a game this coming weekend but they return to action on March 19 when they host third-placed Blackheath, who are just one point ahead of them in the table now.