Frenchman Bosc scored a superb individual effort, while Greenshields provided a dangerous link in attack playing a part in three Dragons’ tries.
But the second half became more free flowing and it took just three minutes for Pelo to grab his second after the interval.
On the final tackle, the 25-year-old picked the ball up and firstly chipped the line of the defence before regathering and then had the skill to chip onrushing full-back Will Sharp for a sublime score under the posts.
Luke Gale provided some faint hope again for the Quins as he latched onto a Catalans mistake and raced 60 metres to score despite the attentions of four defenders.
And Casey McGuire wrapped up the emphatic and somewhat cruel victory as the half-time hooter sounded.