Although considered outsiders and surprise quarter-finalists, Maynooth took the game to Naas and deservedly led 0-8 to 0-6 at half-time, with Pierre Ennis chipping in with some important scores.
Maynooth managed to keep that two-point buffer into the final minutes before pressing the self-destruct button.
On 59 minutes, Mellett converted a free following a needless foul and he repeated the trick in the second and fourth of five additional minutes to send the county town into the last four.
On Friday evening, Moorefield booked their place in the semi finals by virtue of a 1-17 to 1-11 win over Clane in a quarter final replay.
The draw for the semi-finals throws up the possibility of an all Newbridge final.
* Kildare SFC semi-final: Moorefield v Athy, Sarsfields v Naas.