Tony Cousins produced a sparkling one-man show to send Rovers a point clear at the top of the National League Premier Division.
Cousins struck a superb hat-trick, including two just before the break to knock the wind out of Drogheda. The first arrived on 42 minutes, when the in-form striker took possession 30 yards from goal and shrugged off the challenge of Drogheda's John Cody before beating Eddie van Boxtel with a low drive.
Three minutes later, Rovers were two up when Derek Treacy took advantage of a slip by Noel Reid to tee-up Cousins who made no mistake from six yards.
And the league's leading scorer capped a superb individual display when he got the third just two minutes from the finish.