Maxi Rodriguez fired Argentina ahead from Javier Saviola's pass before Esteban Cambiasso rounded off a flowing 24-pass move, finishing from 12 yards.
Javier Saviola set up Rodriguez for the second and after Mateja Kezman saw red for a late lunge, Hernan Crespo made it 4-0 from Lionel Messi's cross.
Carlos Tevez rolled home the fifth and then teed up Messi who completed the rout with a low finish for the sixth.
Argentina took an early lead with a beautifully constructed goal that typified their flowing style.
Juan Pablo Sorin's cute backheel opened Serbia up down the left, allowing Saviola to cut inside where he eased a perfect pass into the path of Rodriguez who stabbed a first-time shot past Dragoslav Jevric.
Argentina gave a masterclass of passing skills to double their lead with the sweetest of goals.
They patiently strung together 21 passes before Juan Pablo Riquelme fed Saviola who slipped a pass inside for Cambiasso. Cambiasso knocked the ball into Crespo who backheeled a return pass into the Inter midfielder who thumped the ball home from 12 yards.
Predrag Djordjevic vainly attempted to prompt Serbia & Montenegro from midfield but there was already an air of resignation from his strikers and they were the architects of their own downfall as Argentina scored a third just before half-time.
Mladen Krstajic's attempts to shepherd the ball out for a corner ended in embarrassment as Saviola took the ball off him and cut inside where his shot was parried by keeper Jevric into the path of Rodriguez who scored from a tight angle via the post.
Savo Milosevic provided Roberto Abbondanzieri with his first test in the opening minute of the second half and the former Aston Villa striker was inches away as he lunged at Kezman's knock-back.
Serbia & Montenegro became increasingly frustrated as Argentina strutted their stuff and Kezman boiled over with a wild lunge on Javier Mascherano which earned him a straight red card.
There was even time for Messi to make a contribution as the substitute latched on to Riquelme's quickly taken free-kick and crossed for Crespo to tap in at the far post.
Another substitute, Tevez, scored a fine individual fifth as he beat two defenders in drifting in from the left before rolling the ball in.
Tevez then provided the pass for Messi to run on and beat Jevric at his near post to complete the rout with Argentina's sixth.
Argentina: Abbondanzieri, Burdisso, Ayala, Heinze, Sorin, Maxi (Messi 74), Mascherano, Gonzalez (Cambiasso 16), Riquelme, Saviola (Tevez 58), Crespo.
Subs Not Used: Coloccini, Aimar, Cruz, Cufre, Franco, Milito, Palacio, Scaloni, Ustari.
Booked: Crespo.
Goals: Maxi 6, Cambiasso 31, Maxi 41, Crespo 78, Tevez 84, Messi 88.
Serbia & Montenegro: Jevric, Duljaj, Gavrancic, Krstajic, Dudic, Koroman (Ljuboja 49), Stankovic, Nadj (Ergic 45), Predrag Djordjevic, Kezman, Milosevic (Vukic 69).
Subs Not Used: Basta, Nenad Djordjevic, Dragutinovic, Ilic, Kovacevic, Stojkovic, Vidic, Zigic.
Sent Off: Kezman (65).
Booked: Koroman, Nadj, Krstajic.
Att: 52,000
Referee: Roberto Rosetti (Italy).
Fifa man of the match: Juan Roman Riquelme.
This 6-0 hammering of Serbia and Montenegro is the joint 10th biggest win ever at the World Cup. Substitute Lionel Messi became Argentina's youngest player at the World Cup (18 years and 357 days). Messi also became the sixth youngest goalscorer ever in the finals. Pele is the youngest at 17 years and 239 days.
Roberto Ayala has equalled Javier Zanetti's career record of 102 caps for Argentina. Diego Simeone is the Argentine record holder with 106. Captain Savo Milosevic won his 100th cap. He's the first Serbia and Montenegro player to reach this milestone. So far Milosevic has won 72 caps for Yugoslavia and 28 for Serbia and Montenegro.
Serbia & Montenegro have now lost their last three World Cup matches (against Argentina and twice against Holland in 1998 and 2006). This equals their worst ever run set in 1974 as Yugoslavia.
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