But the visitors were patient and finally made the breakthrough 10 minutes before the break when Hook went over in the corner and Biggar converted superbly to bring them within a point.
With time ticking down, Sam Tomkins kicked over a drop-goal to give the Warriors a one-point lead into the break but that was their final score of the match as the Dragons defence started to dominant in the second period.
Mulligan pointed the resultant free but perhaps crucially, Brian Roper swung over a great long-range effort to cut Tyrone's lead to a point at the break.