Promotion-chasing Rovers' attempt to avoid a third straight league defeat suffered an early blow when Liam Palmer was sent off for a lunging tackle in only the sixth minute.
Porter, on loan from Sheffield United, pounced on an error from goalkeeper Owain Fon Williams to put the relegation-threatened Shrews ahead before Cameron Gayle headed in his first league goal in the second half to seal back-to-back wins on the road.
And after pulling seven points clear of the npower League One drop zone, Turner was relieved to finally secure some breathing space for his side.
"Time will tell how big the win will be, but it's a massive three points for us irrespective of the match," he said.
"Sometimes it's more difficult to play against 10 men - especially a decent side like Tranmere.
"We've kept our shape, kept our discipline and we've had a host of other chances to increase our lead but you can never tell - there's always that edginess.
"There's got to be that concentration - especially from the goalkeeper and the backline - and we've done that."
Speaking about debutant Porter, Turner added: "His contribution was good during the course of the game. He's held the ball up for us, won a few headers and got in behind a couple of times.
"He's there to score goals and irrespective of how the chances come along, he's there on the spot."