Rovers three points away from Europe
Drogheda United 0 Shamrock Rovers 2
Victory at home to Sligo Rovers next Friday will secure European football next season for Shamrock Rovers after the Hoops' comfortable victory over a Drogheda side who had been relegated prior to kick-off at United Park.
Second-half goals from Ronan Finn and Brandon Miele secured the points for Rovers.
And, with fellow Europa League contenders Bray Wanderers held to a draw by Galway, Stephen Bradley's side now need to win only one of their remaining three games to clinch a top-four finish.
First blood almost went to the home side on seven minutes when Shane Elworthy crossed the ball towards Stephen Elliott who hooked a fine effort just over Tomer Chencinski's crossbar.
With one eye unquestionably on tomorrow's FAI Cup semi-final replay against Dundalk, Bradley opted to shuffle his pack and rest some of his more experienced performers.
As a consequence a somewhat makeshift Hoops' line-up seemed to be lacking a spark in the early stages, but they did threaten when James Doona cut in from the right wing and sent a well-struck diagonal effort flashing narrowly wide.
Neither goalkeeper was tested until the 37th minute when Stephen McGuinness dived to his right to keep out another Doona attempt from just inside the box.
However, Rovers were lucky not to fall behind coming up to half-time from the home side's first corner-kick as Sean Brennan's fine delivery was nodded narrowly wide by Elliott.
The visitors finally hit the front seven minutes into the second half with a well-worked goal. Miele collected a Finn pass and the Hoops' captain continued his run to take the return from Miele and slot the ball home from close range for his fifth league goal of the season.
It was pretty much one-way traffic after that and McGuinness finger-tipped a Gary Shaw effort round the post before the insurance goal arrived on 70 minutes, Miele firing home easily after a deft one-two with Finn.
Substitute Sean Boyd will still be wondering how he didn't manage to add to Drogheda's misery on 85 minutes when he slotted the ball wide after latching onto fellow substitute Michael O'Connor's back-heel.
Drogheda United - McGuinness; Deasy, Gallagher, Buckley, Kane; Elworthy, McEvoy (Bayly 67), Purdy, Doyle (Wixted 82); S Brennan, Elliott (Meaney 65).
Shamrock Rovers - Chencinski; Madden, Grace, Webster, Carpenter; McAllister (King 46); Doona, Finn (O'Connor 72), Connolly, Miele; Shaw (Boyd 72).
Ref - D MacGraith (Mayo)