A 66th-minute try from hooker Mike Essex helped Shannon overcome a stern test from Galwegians at Crowley Park.
The game hung in the balance, early in the second half, when 'Wegians full-back Rob O'Beirn kicked two excellent penalty goals to close the gap to 11-9.
But O'Beirn missed an easier attempt on the hour mark and Shannon seized their chance with Fiach O'Loughlin putting Essex over in the left corner. That score added to Richie Mullane's first half try, while Tadhg Bennett kicked eight points.
Scorers:
Galwegians: Pens: Robert O'Beirn 3.
Shannon: Tries: Richie Mullane, Mike Essex; Con: Tadhg Bennett; Pens: Tadhg Bennett 2.
