Luton slipped back to tenth in the table after losing three games in a row.
LRFC’s tries were scored by man of the match Tom Winch, Byron Odell and captain for the day, Matt Yang.
First team manager Steve Evans was not satisfied with the result but highlighted some individual performances.
He said: “The key difference today was poor decision making from Luton.
“There were just too many mistakes, we shouldn’t have that result.
“We dominated in the forwards, but our backline was not so good.
“I thought Tom Winch put in a really big shift today, he did a remarkable job, I was really impressed with that. Also, Matt Yang steeping in to captain the side, was good motivation for the boys.”
The first half of the game was not in favour of the home side. Old Priorians grabbed the lead before Winch answered with a try in the 15th minute (5-7). The visitors added another two tries before half-time (5-17), one while Yang was in the sin bin after receiving a yellow card.
LRFC kept their heads up in the second half and soon Odell added another five points, which was answered by the Priorians a few minutes
Luton dominated the scrums, with experienced players such as Andy Davey and Yang leading from the front and it was Yang who added a third try, converted by fly-half Hamm in the 58th minute (17-22).
The home team continued to put pressure on the visitors.And with a little more control a scrum on the opposition try line in the last minute of the game could have given Luton a match winning score.
However manager Evans remained realistic before the away game against Eton Manor, who are in the top 5 of the league.
He said: “We know it’s going be tough, all we can do is get the best squad we can get and go with high hopes.”