Sexton again converted the 19th-minute try, but was kicking his heels in the sin-bin seven minutes later after kicking the ball away following his try-saving tackle on Jonathan Davies.
The Dragons, who had Raguin sin-binned seven minutes into the second half, conceded further tries to stand-off Ryan McGoldrick and Adam Fletcher to put their lead at risk but Mounis came to their rescue with his late try.
And, after late pressure in which home flanker Jake Abbott was sin-binned, Quins won it seven minutes from time with a penalty try, converted by Evans.