Limavady got off to the perfect start on three minutes with McGonigle playing a neat one-two with Alfie Gaston, racing clear before expertly chipping the ball over Solis-Grogan.
Their lead was doubled on 11 minutes as Philip Lowry regained possession in the middle of the park before finding McGonigle, who blasted to the bottom right-hand corner of the net.
McGonigle completed his hat-trick on 22 minutes, unleashing an unstoppable strike from a 25 yard free-kick, giving Solis-Grogan no chance.
The Roesiders had a chance to further extend their lead before the break as Stephen Lowry's header from Daniel Lafferty's corner was tipped over the crossbar.
Limavady looked to be easing towards a comfortable victory before Oisin Devlin's effort cannoned off the crossbar but Mulvenna was on hand to fire home the rebound on 71 minutes.
Philip Lowry made a brave block on the line to deny Alfie Mitchell from close range as Bangor looked to get back into the game.
Limavady were reduced to 10 with five minutes to play as Stephen Lowry was shown a straight red card for a heavy challenge on Devlin, but the Roesiders held on for a massive three point.