The Giants need a nine-point win in Glasgow next month to earn a place in the BBL Cup final.
Coach Danny Byrne’s men fell to an 85-77 defeat at home – after being within two points of their visitors with five minutes of the first leg of the semi-final to go.
The Giants had the worse of a scrappy first half, with Glasgow 40-32 up at half-time.
But they fought back with more composure after the break, taking the third quarter 22-20 before the Rocks had the better of the final minutes.
Ingus Bankevics led the way for the Giants with 17 points, while Mike McCall Jr had 14 and Willie Clayton 13 and 18 rebounds for another double double in a tough battle with Kieron Achara.
The big Scot had 22 for the Rocks while his team-mate Bouna Ndiaye hit 24 as a thorn in the Giants’ side.
Byrne said: “I’m happy with our performance in the second half which was much better than the first.
“It was a messy first half and we go to Scotland with a tough job to do. But we are capable of doing it and we have been good on the road this season.”
The return leg of the semi is in Glasgow on January 13. Newcastle Eagles lead London Lions by two points in the other last-four game.
The final aggregate score of each semi decides who progresses to the final in Birmingham.