Roberts was run off a field goal before kicking in haste in the final minutes, while Bulldog Moses Mbye managed to get one off, but it was charged down by Ryan James.
Josh Morris picked up the ricochet with 30 seconds remaining, and took a stab that missed.
The Bulldogs had earlier taken a six-point advantage into halftime, despite Titans back-rower Zeb Taia nabbing first points in the ninth minute.
Tries to both Bulldogs wingers, Sam Perrett and Curtis Rona, helped gain the lead, before Mbye found Will Hopoate for a third try just before the break.
Bulldogs 21 (W. Hopoate, J. Jackson, S. Perrett, C. Rona tries; K Holland 2 goals, J Reynolds field goal) Titans 20 (J. Hoffman, D. Mead, Z. Taia tries; T Roberts 4 goals).
The Kangaroos will reportedly name their team five days early in a bid to gain an edge over New Zealand ahead of next month's Anzac test in Newcastle.
After three straight losses to the Kiwis, the Kangaroos are set to break with tradition and name their test squad on Tuesday. The team announcement had been scheduled for Sunday, May 1.
The rationale behind the move is to give new coach Mal Meninga the opportunity to get his players into camp up to 48 hours earlier in preparation for the Hunter Stadium test.