Lawson was on Thursday named at scrum-half and captain for the clash - continuing as skipper after extending his 100% record when leading the side in the 15-6 defeat of Georgia - in a side showing five changes.
Head coach Andy Robinson opted not to recall tournament captain Alastair Kellock, with Richie Gray instead brought into the second row alongside Jim Hamilton, while Geoff Cross, John Barclay, Ruaridh Jackson and Chris Paterson also returned.
Lawson said: "We certainly believe that it's a game we can win. We're fully aware that we need to improve our performance from the first game and from the second game and it's going to be a big step up in the challenge.
"But it's one that we're relishing and one we've looked forward to for a long time.
"We want the game to be played at pace, we're aware that they're a big pack and we want to move them around, make them tackle and make them get up again and again."
Kellock, who was captain in the opening 34-24 victory over Romania, was a victim of the intense competition at second row.
His Glasgow Warriors team-mate Gray and Gloucester's Hamilton were preferred, while Nathan Hines, who can also play back row, was named on the bench.
Lawson, who has won all four games in which he has captained Scotland, said: "Al's obviously gutted, as everyone who isn't involved is.
"At the same time he's a great guy, he came across and congratulated me and said he felt I deserved it and good luck.
"He wants the squad to do well - there's no doubt about that - and I'm sure he'll bounce back and train well and selection opens up for the England game (on October 1).
"This is a 30-man game at World Cups. Everyone has to play a massive part within that.
"We've been waiting for this selection - everyone's had it in the back of their minds for some time.
"Ultimately, we have a collective responsibility now to put in a huge performance for the entire squad.
"Andy's made his selections and now it's time for the guys who have been selected to step up and put in a huge performance for Scotland."
Scotland are seeking a sixth successive win on Sunday - a feat not achieved since the 1989-90 Grand Slam-winning season - and one which would ensure they maintain their record of progressing to the knockout stages at every World Cup tournament.
At the quarter-final stage in 2007 it was Argentina who beat Scotland.
But Scotland have won three of the five fixtures between the sides since, including a 2-0 Test series win in South America in June 2010.
Lawson began the match in Tucuman and the fixture the following week in Mar del Plata, but believes the Pumas are now a different proposition.
The Gloucester scrum-half added: "The Argentinian team in a World Cup is a slightly different beast to what it is on a summer tour, just due to the length of time they have together and to prepare.
"They will be more organised, but equally I think we are too.
"We expect them to be physical, we expect them to make a mess at the breakdown, they're a very good defensive side and they're very direct in attack.
"As they showed against Romania, given time and space they'll take opportunities and have the ability to score tries."
Outside Lawson at fly-half is Jackson, who has been tasked with leading Scotland's three-quarter line and releasing centres Graeme Morrison and Nick De Luca, wings Sean Lamont and Max Evans and full-back Paterson, who has been recalled in place of Rory Lamont.
Barclay has replaced Ross Rennie at openside flanker in what Robinson suggested was a tough call - but Barclay has played against the Pumas three times and is yet to taste defeat.
Cross has been recalled at tighthead prop in place of Euan Murray, who is unavailable due to religious reasons as the match falls on a Sunday.
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