Harps went ahead thanks to a Packie Mailey effort that was adjudged to have crossed the line following a goalmouth scramble on 29 minutes.
Cobh had a great chance to get back into the game on 44 minutes when Kynan Rocks was taken down in the box by Damien McNulty but Ciaran Gallagher got down to save Stephen Kenny’s penalty.
Harps remained on top after the break with Nathal Boyle and Kevin McHugh both going close.
Cobh had Brendan Frahill sent off in the 87th minute for a rash challenge on Wilfried Tagbo.
Tagbo then tapped in a McHugh cross in stoppage time to make it 2-0.
Meanwhile, Derry City were held to a scoreless draw in their Premier Division clash against Limerick FC at the Brandywell.
City missed a number of chances to bag the points but the battling basement visitors will feel they were worth a share of the spoils.
But this latest poor result means that City continue to flirt with relegation and remain second bottom.