Gareth Taylor scored the only goal of the game, after Calvin Zola chased down a clearance from visiting keeper Julien Baudet, but the Wirral side spurned several chances to give themselves a greater winning margin.
But they still moved up to fifth in the League One table, leaving them back on course for a tilt at the play-offs.
"We were desperate for a result and we are back in there now in fifth place," beamed Moore.
"In the end we were left hanging on a bit ,but we thoroughly deserved the victory.
"We have got to be pleased with the way we performed and tactically we were very good."
Tranmere's players have little time to recover from the match, as they host Bradford City on Friday night.