The visitors took the lead shortly before the break when Mensur Kurtisi arrived late in the box to tuck home Henrique's cutback.
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The Glory were handed a route back into the game within four minutes of the restart as Jade North hacked down Keogh inside the box, and the former Republic of Ireland international coolly dispatched the resulting spot kick.
However, they were level for little more than five minutes as Henrqiue restored the Lionhearts' lead with a powerful drive from the edge of the box.
Perth poured forward in search of an equaliser, which came in the 74th minute as Keogh's heavily-deflected strike wrongfooted Jamie Young and span into the back of the net.
With the game deep in stoppage time, Keogh rounded off a man-of-the-match display as he nodded the ball into the corner of the net to make it 3-2.