The narrowness of the scoreline should not however bely the superiority of the South Americans, who were comfortable in possession and in control throughout the game.
The fixture had clearly captured the imagination of the media rather than the paying public, there being just 32,492 spectators inside the oval bowl
There were three Rangers players in the Scotland side - namely Allan McGregor, Kirk Broadfoot and Barry Ferguson (captaining his side for the 27th time), with former Ibrox man Alan Hutton also in the starting line-up.
It was the visitors who made the early running - Rodriguez's volley from Javier Mascherano's flick being turned away by McGregor in five minutes.
Two minutes later the opening goal arrived when Carlos Tevez played the ball to Jonas Gutierrez who turned the ball into the path of Rodriguez who slotted the ball home.
The South Americans were in command - Tevez, through on a Gutierrez pass, was denied when McGregor blocked his effort with his legs in eighteen minutes.
Argentina had totally dominated the opening half-hour, but just to prove that it was not all one-way traffic Paul Hartley's corner, head-flicked on by Kirk Broadfoot, saw Stephen McManus head over.
Broadfoot himself was inches away from connecting with a Kris Commons free-kick in 33 minutes, then eight minutes later Jamie McFadden dispossessed Martin Demichelles following Chris Iwelumo's knock-on only to see Argentinian goalkeeper Juan Pablo Carrizo parry his effort.
The visitors were a class apart despite their slender lead - underlined in 57 minutes when Manchester United's Carlos Tevez embarked on a solo run through the heart of the Scots defence before sending his shot from the edge of the box just over.
Chances were few and far between during the second-half - home substitute Lee Miller's header from a Shaun Maloney corner drifted wide in 71 minutes, then three minutes later a Gabriel Heinze free-kick from 22 yards just cleared the crossbar.
Argentina were seldom threatened however, ending the game comfortable winners despite having just the one goal to show for their superiority.
Afterwards the iconic Maradona summed up his first game in charge:
"We had a clear victory. My side was brilliant for the first 25 minutes, but did not convert enough chances. We kept control throughout the game and deserved the win. I am a proud man tonight - our performance filled me with pride and hope for the future. My lads made things easy for me and wore the shirt with pride. There is great spirit in the squad - my players would give their lives for the shirt."
Maradona took time out to praise the Scots:
"Scotland are a fine side with good players - but technically we were better."
Meanwhile Scotland Manager George Burley was understandably more cautious:
"We were playing against one of the best sides in the world. Argentina dominated in the first 25 minutes but we held our own thereafter. We can take positives from tonight - it was a worthwhile experience. It's always great to pit your wits against the best. We came out of the game with credit."
SCOTLAND McGregor (Rangers); Hutton (Tottenham Hotspur), Broadfoot (Rangers); McManus (Celtic) [Berra (Hearts) 74], Caldwell (Celtic), Ferguson (Rangers) [Robertson (Dundee United) 58]; Brown (Celtic) [Alexander (Burnley) 82], Hartley (Celtic) [Maloney (Celtic) 58], Iwelumo (Wolverhampton Wanderers) [Miller (Aberdeen) 45), McFadden (Birmingham City) [Clarkson (Motherwell) 66], Commons (Derby County)
UNUSED SUBS Marshall (Norwich City), Naysmith (Sheffield United), Barr (Falkirk), McAllister (Bristol City)
ARGENTINA Carrizo (Lazio); Demichelis (Bayern Munich), Papa (Velez Sarsfield) [Diaz (Getafe) 85], Gago (Real Madrid), Heinze (Real Madrid), Lavezzi (Napoli) [Denis (Napoli) 74], Zanetti (Internazionale), Tevez (Manchester United), Mascherano (Liverpool), Rodriguez (Atletico Madrid) [Sosa (Bayern Munich) 90], Gutierrez (Newcastle United) [Gonzalez (Porto) 70]
UNUSED SUBS Romero (AZ Alkmaar), Coloccini (Newcastle United), Villagra (River Plate), Burdisso (Internazionale), Lopez (Porto), Montenegro (Independiente),
REFEREE Felix Brych (Germany)