Ryan Prosser marked his return from injury with a 12th minute goal, which was the first of three scored by The Martyrs.
Prosser followed up after Gosport goalkeeper O'Flaherty parried a shit from Ian Traylor. Lee Lucas forced a good save after that as Merthyr Town dominated the game and took a 1-0 lead into half time.
Ian Traylor finished off a fine move to make it 2-0, and Kieran Lewis crowned the win by adding a third after a fine run and cross from, Corey Jenkins.
Goalkeeper Scott Reed had to make a sharp save low to his right, but apart from collecting a couple of corners was largely untroubled. Craig McDonnell made a welcome return from injury after dislocating his shoulder on New Year's Day against Taunton Town.
Brief highlights are available on the club's YouTube channel, which you can access by clicking here.