The West Country visitors had dominated the game throughout and were desperately unlucky to concede at the death despite the home side's late rally.
It was home keeper Sam Russell who was the busier throughout the 90minutes as he repelled the Pirates time after time. Russell denied Richard Walker on two occasions in the opening period of the game as the visitors ran amok.
Resolute defending from home captain Patrick Collins kept Rovers at bay, but the hosts were dealt a blow when he had to be replaced after suffering an injury in the 32nd minute.
The visitors continued to dominate and Ricky Lambert went close with a 25-yard free kick before the home side rallied in the 43rd minute when Martin Smith went close.
Soon after the restart Darlington striker Julian Joachim tested Rovers keeper Steve Phillips, but it was a brief rest bite as Rovers took the lead soon afterwards. Lewis Haldane peeled off his marker inside the area and fired high into the net from 12 yards out to give the visitors a deserved lead on 53 minutes.
Three minutes later Phillips was in action to save a close range header from Kalusivikako Ngoma comfortably, as the home side looked to get back into the game. But in the 66th minute it was Russell who was busy again as he denied Rovers substitute Chris Carruthers.
Darlington then brought on striker Alun Armstrong and the substitute was soon in the thick of the action with a 35-yard lob which came back off the crossbar in the 70th minute.
The home side rallied late into the game but it looked as though missed chances from Michael Cunnings and Julian Joachim had left the home side too much to do.
However as the game entered its dying moments there was some cheer for the home fans when Smith fired in a rasping drive from just inside the area when he connected with a cross from substitute Neil Wainwright.