Scrumhalf Ben Youngs came on as second-half replacement and offered the spark that England had missed, finding a rare gap in the defence and darting over for the only try of the Pool B encounter.
Argentina should have been out of reach after England conceded a string of penalties at the breakdown but five missed kicks by Martin Rodriguez and one by Felipe Contepomi kept the Six Nations champions in touch despite a miserable kicking performance by Jonny Wilkinson.
"It's blindingly obvious that we could easily have lost that game," England team manager Martin Johnson said. Still, it's the outcome that matters.
"Do I think we're a fair winner?" he said. "We're the winner. We scored more points and that's how we decide it."
Wilkinson converted for 10-9 to put England in front for the first time after 66 minutes and then landed a penalty to complete the scoring in the 74th, but the usually reliable flyhalf missed five kicks of his own under the glass roof of Dunedin's Otago Stadium.
"I don't even know how many I missed," Wilkinson said. "I'm not going to apportion any kind of blame other than to myself. I'm the one kicking the ball."
But Wilkinson wasn't alone. Between them, the rival teams succeeded with just six of 17 place kicks in the unique sealed environment.
"He said he just couldn't get the control on the ball," England captain Mike Tindall said. "He said he was hitting it well, but couldn't control it."
Until Youngs' intervention, Argentina seemed set to open the World Cup with a shock win for a second straight tournament. Four years after beating host France in an opening night upset, Argentina dominated the setpiece and breakdown against England with No. 8 Juan Martin Lobbe earning the man-of-the-match award.
Aside from one 40-meter (yard) break by fullback Ben Foden midway through the first half, England showed little enterprise. Without England figuring a way around them, Lobbe and Julio Cabello not only prevented the English from making ground but continually drove them back when they took the ball into contact.
England openside flanker James Haskell seemed to suggest to the referee that the physicality had spilled over into gouging, but said after the match that the Pumas had just about kept things legal.
"At the last breakdown, I got a bit het up," said Haskell, sporting a huge purple bruise under his left eye. "I got cleared out. I had hands in my face and I think it was just a bit of over-exuberance in the end. In the heat of the moment you react as you do."
Argentina could have been 18-6 ahead at the break had Contepomi and Rodriguez landed all their kicks rather than landing just one each.
"We said before we came, that's what World Cups are about," Johnson said. "You'll be in a game where it's not going your way, probably getting a few penalties against you, the bounce of the ball seems to be not favouring you and you've got to find a way to win.
"And we did."
Having spent much of the buildup to the match highlighting their improved discipline, England failed to heed referee Bryce Lawrence's early warning for conceding three penalties in the first four minutes. Lawrence eventually sent prop Dan Cole to the sin bin in the 34th minute, giving Argentina a one-man advantage.
Argentina started the second half ferociously against England's 14 men but two try-scoring opportunities following breaks by Rodriguez and replacement flyhalf Marcelo Bosch yielded only a penalty by Rodriguez for 9-3 by the time Cole returned.
At least England got their man back. Argentina's Contepomi and Gonzalo Tiesi were both carried from the field in the first half with serious looking injuries.
"I won't know for sure what the injury is until I go to the hospital for an X-ray," Contepomi said. "It could be a cartilage, it could be a rib."
Prop Rodrigo Roncero had already been off for treatment on his bleeding head when Contepomi departed after receiving lengthy treatment as played continued around him.
Tiesi was then helped off by medics after writhing in pain with a suspected knee ligament injury sustained in a tackle, with a replay of the incident on the big screens at Otago Stadium drawing gasps from crowd.
Argentina's exertions began to tell with gaps opening up and Youngs, who replaced Richard Wigglesworth in the 50th, showed what England had missed when he sat out its three warmup matches injured.
Until then, it had been the Pumas who came closest to a try, with veteran hooker Mario Ledesma, prop Juan Figallo and then Cabello held up on the line.
Ledesma tried to crunch his way through, Figallo was blocked on the ground just short and Cabello tried to leap over a pile of bodies before Lawrence pulled play back for an earlier offside by Steve Thompson.
England's best opportunity at that stage had come when, with captain Contepomi down, Foden made his break. Upended by last man Cabello, he threw out to Delon Armitage, who hesitated before starting for the line and was caught.
"The best thing about it from my point of view is that no one panicked," Tindall said. No one got stressed and we just carried on. Once we played the sort of rugby we wanted to play, we got under the sticks."