Glamorgan 274 for 9 (Lloyd 59, Labuschagne 51, Cullen 50, Finn 5-64) trail Middlesex 410 (Stirling 138, Robson 107) by 136 runs
Middlesex and Glamorgan look destined to share the spoils in Radlett's inaugural County Championship fixture after rain restricted them to 48 overs on day three.
The prospects of a positive result rested mainly on Middlesex forcing the visitors to follow on, but Glamorgan's ninth-wicket pair scrambled beyond that landmark to close on 274 for 9, still 136 runs adrift of their hosts' total of 410.
Captain David Lloyd led the way with a knock of 59, ably supported by Tom Cullen in a sixth-wicket stand of 86 before Graeme Wagg's unbeaten 37 hauled Glamorgan away from danger.
Middlesex made it difficult for Glamorgan, with their attack spearheaded by a hostile display of fast bowling from Steven Finn, who recorded his first five-wicket haul of the campaign.
Glamorgan resumed at 112 for 3 in the morning, but soon found themselves under pressure after Finn captured two early wickets in a ferocious opening spell.
The Middlesex seamer unleashed one rising delivery that almost cut Billy Root in half before his next ball, a gem of a yorker, uprooted both the off and middle stumps. In his next over, Finn persuaded Owen Morgan to edge an outswinger into the gloves of John Simpson, reducing Glamorgan to 118 for 5.
However, Cullen looked lively as he dispatched George Scott through the covers twice and, with Lloyd also scoring freely, the pair thwarted Middlesex's hopes of getting among the tail.
The Glamorgan skipper progressed to his half-century, but his was the only other wicket to fall before lunch as he attempted to pull Finn and spooned the ball into the hands of Tom Helm.
Cullen followed after a brief rain delay, completing his third Championship half-century in five games before Paul Stirling's introduction brought about two wickets in an over.
The off-spinner produced a ball that climbed on Cullen, who could only send it looping into the hands of close fielder Stevie Eskinazi, and he then tempted Marchant de Lange into a big heave that was taken at deep mid-wicket.
At that stage, Glamorgan were still 28 runs short of avoiding the follow-on, but Wagg and Lukas Carey dug in and gradually brought that deficit down.
Wagg began to cut loose, driving Nathan Sowter over cover for six, but the leg-spinner was unlucky not to remove Carey in his next over, with the diving Sam Robson unable to cling onto a sharp chance at slip.
The pair ran two to finally banish all threat of the follow-on and, although Finn snatched his fifth wicket when Carey slammed him to Scott at backward point, the heavens opened again soon afterwards. Umpires Graham Lloyd and Neil Bainton eventually abandoned play for the day at 5pm.
