The 19-year-old produced a spell of 5-3 in 19 balls as six Glamorgan wickets fell in the last 13 overs of day one.
Ben Cox's aggressive 93 off 99 balls was the mainstay of the home innings, while Ed Barnard (60) and Tongue (41) led the lower-order resistance.
Timm van der Gugten, with 4-66, was the pick of the Glamorgan attack.
Worcestershire counter-attacked hard from their poor start as Cox, having come in on a hat-trick on 14-3, hit 15 fours before being brilliantly caught by Andrew Salter within sight of his century.
After two double century opening stands in three matches, this time both Worcestershire openers were back in the pavilion inside eight overs, Daryl Mitchell, who had scored 534 runs in his previous five innings, going for a third-ball duck.
Netherlands seamer van der Gugten claimed four of the first six wickets to fall in an accurate display, including Tom Fell and Brett D'Oliveira in successive balls.
But, in only his sixth Championship game, Tongue outshone everyone. He improved his best with both bat and ball, aided by some superb slip catching in the dramatic closing overs as only Jacques Rudolph (49 not out) reached double figures.
Worcestershire's Ben Cox told BBC Hereford & Worcester:
"It was an edgy start, going in at 14-3, and I wasn't backing myself. But, on a wicket like that, it sometimes suits my game to go out and try and put the pressure back on them.
"Fortunately my edges didn't go to hand. And iIt was a good catch (to get me out), but it's 93 from a position where we were really struggling and we're in a good position now.
"We couldn't be happier after that spell from Tonguey. That's one of the best spells I've kept to. We said it down at Glamorgan that there's going to be times that he has those spells, he clicks and hits the zone."
Glamorgan's Jacques Rudolph told BBC Wales Sport:
"First and foremost it was a great spell of bowling (by Tongue), it's one of those spells where Joe (Clarke) took a brilliant one-handed catch, the keeper (Cox) took a brilliant one-handed catch and it's obviously not ideal to be in this position because it's quite a good wicket.
"Coming back, we've got to have a strong mind-set and when we bowl again. we probably gave 20 to 30 runs too many, but there's still plenty of time left in the game.
"If your mind-set's good on this wicket, it gives you opportunities to score, Cox almost got a hundred by playing really positively."

Those arrested include two builders, police officers and municipality officials.
The apartment building came crashing down on Thursday.
Correspondents say building collapses are common in India, with poor construction practices often blamed.
In pictures: Mumbai building collapse
There is huge demand for housing, and corruption often leads to cost-cutting and a lack of safety inspections, correspondents say.
Police commissioner K P Raghuvanshi said the builders were arrested for allegedly paying bribes to police and municipal officials to construct the building in the Mumbai suburb of Thane without any official sanction.
Mr Raghuvanshi said on Sunday that the nine would be formally charged with culpable homicide and causing death by negligence, once the investigation into the accident had been completed.
If convicted, they face sentences of up to life in prison.
Most of the victims of the Thane collapse were poor daily wage earners working at the site, and their families. The dead included 30 children and 18 women.
Building work had continued at the block even though four floors were already occupied.
One police official told the BBC that the collapse appeared to have been caused by the use of substandard building material.
Witnesses said the construction of the building started just six weeks ago, since when seven floors had been built. The eighth floor was under construction.
In a similar collapse in 2010, 69 people were killed in Delhi.
Worcestershire's teenage seamer Josh Tongue tore Glamorgan apart with five wickets as they fell to 76-6 in reply to the hosts' 267 all out at New Road.
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Indian police have arrested nine people they suspect of colluding to illegally construct a high-rise residential building in Mumbai which collapsed, killing 74 people.