Richards converted from 12 yards after Marvin Morgan was brought down in the area by Ben Davies to leave Preston without a home win in the league since September.
The Lilywhites looked like they were going to end that run when Stuart Beavon scored his ninth of the season after 43 minutes but Jon Taylor equalised and Richards wrapped it up.
Victory saw the struggling Shrews close the gap on Preston in 17th to just a point and move eight points clear of the drop zone with Turner admitting his side now had room to breathe.
"The win just hasn't sunk in yet but it was a really hard battle for us out there. We knew what to expect when we came here and it was hard work for us," said Turner.
"We stuck at it and we showed real character to come back after going a goal down - it was terrific to see.
"In the first half I don't think our goalkeeper Chris Weale had a save to make and then for their lad to hit one from that range right into the top corner just before half-time was a real body blow.
"We have to be pleased and that is a real release of pressure ahead of the Sheffield United game. It doesn't half lighten the load on the players as well.
"It took a lot of character from Matt to step up and show such composure for the penalty."