Saracens hooker Dan missed a front-on tackle on Santiago Carreras for the Pumas fly-half to race in for a crucial try at the Stade de France.
Dan atoned immediately though, also gaining revenge on Carreras in the process.
The 22-year-old raced through from the restart, charged down fly-half Carreras and followed up to dot down a try of his own.
Nicolas Sanchez had a chance to draw Argentina level with six minutes to play, but the former Toulon fly-half hooked his effort wide and England held out.
Ben Earl had put England into a commanding early lead with a smart try, while captain Owen Farrell ended the night with 16 pivotal points from the boot.
Ben Youngs can now retire from Test rugby with a job well done, albeit with a performance he would surely accept was patchy at best.
But with an England men’s record 127 caps, his Red Rose contribution will endure across the ages.
Dan Cole and Danny Care saw England across the line at the death, and the two veterans will likely follow Youngs with this clash proving their last Test outing.
England’s punishing semi-final with South Africa just six days earlier eventually took a clear toll on the Red Rose men.
The resurgent England had to empty the tank and then some to push the Springboks all the way last weekend, only to lose out 16-15 in agonising circumstances.
This week it would be England who held on though, and now Steve Borthwick’s men will at least return home with pride intact and medals in their pockets.
Borthwick’s side started at breakneck speed, but could not sustain that tempo, physicality or dominance.
Earl raced home from a stunning straight line, scything through from deep, albeit amid precious little Pumas resistance.
Farrell converted and added three penalties in a first half where England should have been in total control but where they instead fell off the pace slightly.
An overhit Youngs box kick allowed Argentina a foothold, and that was enough to change the momentum. The Pumas pounced, and suddenly came alive.
Marcus Smith failed to handle two high balls at the back, and the ultimate fruit for Argentina was a smart try from Tomas Cubelli.
Emiliano Boffelli converted to add to a penalty, to leave England leading 16-10 at half-time.
England lurched from disaster to immediate recovery after the interval. Dan missed a straight-up tackle in the defensive line, and Santiago Carreras raced in for a cheap score.
Boffelli’s conversion stole Argentina a 17-16 lead – that they could only hold for two minutes. Dan charged down fly-half Carreras straight from the restart, and raced in for a redemptive score.
Farrell’s conversion put England back into a 23-17 lead. Boffelli quickly drilled a long-range penalty to cut that advantage in half however, to tee up a tense final quarter.
England unloaded their bench, pairing George Ford at 10 with Farrell at 12 as Manu Tuilagi was withdrawn.
Smith continued at full-back to leave England with three playmakers strewn across their backline.
The Harlequins star finally found the groove with a cute grubber into the Argentina 22, so good as to force an England lineout with Juan Cruz Mallia hustled into touch.
Ford-Farrell-Marchant lacked a straight-dart direct threat though, and the Pumas easily defended England’s structured attack.
England won a scrum penalty, with the new front row of Bevan Rodd, Jamie George and Dan Cole heaping on the pressure.
Farrell slotted the penalty to move England into a 26-20 lead, amid further booing from the crowd.
No one booed when Sanchez slotted a penalty for the Pumas three minutes later however, to trim England’s lead back to three points.
Argentina continued to press and England continued to gift them routes into their attack.
Sanchez scuffed a penalty wide however, that would have levelled the match with six minutes to play. Still Argentina flew at England, more energised and more urgent.
Mateo Carreras zipped clear down the left as England ran out of numbers, only for Ford to produce a try-saving tackle of ultimate bravery.
A free-kick and a penalty from two scrums later, and England were home and hosed.