After resuming on 48-1, in reply to table-topping Lancashire's 462, Glamorgan had slipped to 182-6 when the threatened downpour arrived 19.2 overs into the afternoon session.
It leaves Glamorgan still 280 behind going into the final day.
Their first target will be the 131 runs they still need to avoid the follow-on.
The patience of Lancashire's bowlers was rewarded as the home side took five wickets, two of them for for Australian all-rounder James Faulkner and two for 41-year-old veteran Glen Chapple, who is now within 18 of reaching a career haul of 1,000 first-class wickets.
Nightwatchman Andrew Salter was Glamorgan's top performer with 45 before being stumped by Alex Davies off Simon Kerrigan.
Lancashire now need to take 14 wickets in the final three sessions if they are to win this Division Two promotion clash on Monday and take a major step closer to promotion back to Division One.
Lancashire veteran Glen Chapple told BBC Sport:
"We've played well in this game. We laid a foundation in the first couple of sessions and gradually we increased the scoring rate and put ourselves in a strong position.
"The pitch was slow to start with. Our batters tried to wear them down and we did that successfully, then Alex Davies and Jimmy Faulkner really picked up the rate on the second day.
"I also think we bowled pretty well. I don't know if I'm leader of the attack but it's nice to be involved and I'm enjoying my cricket.
"We've got them at 182-6 and there's a chance of enforcing the follow-on. To take 14 wickets on there will be a good effort but, if we can take four in the first session, that'll give us a chance."
Glamorgan all-rounder Andrew Salter told BBC Wales Sport:
"This game, we really wanted to hit it running and it hasn't quite happened for us. With them scoring over 400 it wasn't the ideal start with us fielding 140 overs.
"But it's important we just do things right and finish this game strongly. We've still got quite a lot of batting to come with the likes of Graham Wagg and Mark Wallace, so we should be able to post a good total.
"I've been working quite hard on my batting with our head coach Toby Radford and it was a good challenge coming in as nightwatchman.
"I felt good. I'd have liked to score a 50 and then kick on again for 100, but unfortunately not."
Heavy rain wiped out the second half of the day's play at Old Trafford after Lancashire had bowled themselves into a winning position against Glamorgan.