The Frenchman, on loan from Norwich City, shone for Ray McKinnon’s men with his second-half double, having gone out of the League Cup quarter-final to the Ton a few days earlier.
“This time it’s me who’s scoring, but on another day it could be someone else,” said Andreu afterwards.
“To be honest, it doesn’t really matter who scores. I’m delighted to score, but I just want to do my bit for the team.”
It was a slow start but the Greenock outfit came within inches of taking the lead in 38 minutes.
The United defence failed to deal with a corner and from the rebound on-loan Celtic ace Aidan Nesbitt’s shot beat Cammy Bell, only to come back off the post.
From the rebound, Thomas O’Ware struck his shot over the bar from 12-yards as the hosts breathed a sigh of relief.
However, United made the breakthrough in 64 minutes.
Substitute Tope Obadeyi swung over a cross from the right for Andreu, whose 12-yard effort was on target and Andy McNeil couldn’t keep it out.
And, in 90 minutes, Murray’s head-flick on was met by Andreu and he made no mistake with a close-range finish, before United substitute Sean Dillon forced an own goal in injury-time when he converted into his own net from Ross Forbes’ free-kick.
Jim Duffy, the Morton manager, said: ‘I’m gutted. I don’t think we deserved to lose.
“It’s a travesty. We were the better side first-half.”