Yetton's second-half spot-kick brought the hosts level following a Rob Farkins strike eight minutes before the break.
The Terras were arguably the better side on the day, even with a player short after Chris Shephard was sent off late in the first period for lashing out at Farkins.
Player-manager Jason Matthews made two changes to the Weymouth side that started the victory over Arlesey, with Jamie Laird and Tim Sills coming in for Sam Poole and Alec Fiddes.
Truro featured a number of former Weymouth and Dorchester players in their squad and the only change for them after a 5-0 thumping of Bideford on Boxing Day saw Dan Green replace Arran Pugh.
Ex-Magpie Green was involved in the game's first flashpoint when he went in strongly on George Rigg, though there did seem to be a bit of a delayed reaction from the latter.
There wasn't much to separate the sides in the opening 10 minutes and the only threat on either goal came when Truro's Craig Duff fizzed over a dangerous cross that just eluded his team-mates in the middle.
The dearth of scoring opportunities continued as the match entered the second quarter and there was very little for the crowd to get excited about on a cold and breezy day.
That was until the 27th minute when City stopper Charlie Burns failed to deal with a ball into the visitors' area and only a last-ditch intervention by one of his defenders prevented a Rigg volley finding the net.
It didn't look the deadlock would be broken before the break, but on 37 minutes the Cornish outfit took the lead.
Weymouth failed to clear a corner, the ball dropped to defender Farkins and he rifled a shot past Matthews with the aid of a slight touch off a Terras' player.
Then, pretty much out of nothing, it all kicked off.
Shephard was shown a straight red by referee Richard Corp for his part in an altercation with Farkins that left the Truro man on the deck.
Chris McPhee picked up a booking following the melee that resulted in his team-mate's dismissal.
With the hosts clearly shaken by Shephard's sending off, Rigg was cautioned on the stroke of half-time for saying something out of turn to the Frome official.
The referee was having a busy afternoon and just two minutes into the second half he booked Farkins for hauling down Sills after the Terras' striker had got the better of him.
Sills then had half a chance to draw the home side level but his glancing header from Rigg's cross went wide.
At the other end, Danny Greenslade fired a free-kick just past Matthews' left-hand post and Isaac Vassell nearly converted an excellent Shane White centre.
Both sides then made their first substitutions of the encounter. Alec Fiddes replaced Jake Wannell for the hosts while Truro swapped Farkins for ex-Terra Shane Krac.
And just minutes after the changes were made the Terras found an equaliser.
Skipper Yetton was heading away from goal when a clumsy challenge on the edge of the City box from Greenslade saw the referee point to the penalty spot on the advice of his assistant.
And Yetton, who has been so deadly from 12 yards of late, coolly converted the spot-kick past Burns.
However, the visitors came within inches of regaining the lead seconds later, only for Vassell to just miss White's low ball across goal.
The last quarter of a largely disappointing game was just like the first - very few scoring opportunities for either side.
But credit has to go to Weymouth for the way they battled with 10 men, and they may even have won it in injury-time.
Yetton played in Steve Colwell down the left and his cross only just evaded a Weymouth player at the far post.
They may have missed out on a 10th straight Evo-Stik Southern Premier Division victory, but the Terras could take a lot of heart from this draw against one of their promotion rivals.
Weymouth: Matthews, Wells, Wannell (Fiddes 60), McPhee, J Laird, Colwell, Kelly (Copp 79), Rigg, Yetton (capt), Sills, Shephard.
Subs (not used): West, C Laird, Will.
Red card: Shephard
Yellow cards: Cooke, Farkins, Ash.
Goals: Farkins (37) 0-1, Yetton (65) 1-1.
Referee Richard Copp (Frome).