Despite an embarrassment of attacking riches, Alejandro Sabella's side struggled to create clear-cut chances against a dogged Romanian defense in Bucharest, and the hosts were unfortunate to see Alexandru Maxim's first-half goal disallowed.
Maxim fired home at the back post after collecting a superb cross from Alexandru Matel 10 minutes before halftime, only for referee Gianluca Rocchi to rule the effort out after his assistant inexplicably flagged for an infringement.
As an out-of-sorts Lionel Messi - who appeared to vomit on the pitch shortly after kickoff - toiled, Sergio Aguero offered Argentina's main threat. The Manchester City man was foiled by stoic defending on three occasions before being withdrawn early in the second half.
Messi had the first effort on goal with a 25-yard free-kick that was deflected wide after four minutes, but Romania grew in confidence as the visitors' captain and talisman struggled to exert his usual influence.
After Gonzalo Higuain had a shot smothered by Ciprian Tatarusanu, the hosts began to carve out chances, with skipper Ciprian Marica forcing Sergio Romero to tip his looping header over the bar on 21 minutes.
Romania was served a reminder of the firepower at Sabella's disposal when Aguero's effort from Higuain's cut-back was blocked, although it was the hosts who spurned the best chance of the first half in the 33rd minute.
Matel's superb delivery from the right was met with a thumping header from Maxim, which was somehow kept out by Romero from point-blank range.
That same duo combined again shortly after for the game's main talking point, as the assistant referee decided that Maxim's well-taken left-footed shot should not stand.
Aguero provided a moment of real quality six minutes before the interval, as the forward surged past three defenders only to see his effort from 10 yards well saved by Tatarusanu.
City striker Aguero again went close almost immediately after the restart as he raced onto Javier Mascherano's through ball and rounded club-mate Costel Pantilimon - who replaced Tatarusanu at the break - only to see his shot from an acute angle blocked by Florin Gardos.
Sabella elected to withdraw Aguero for Rodrigo Palacio just before the hour, and with him went much of Argentina's attacking threat.
However, it was Palacio who missed Argentina's best chance of the match shortly after when he side-footed wide form close range, before Angel di Maria looped a shot over after latching on to another splendid Mascherano pass.
Pantilimon was again called into action in the closing stages as he produced an incredible stop to divert substitute Ezequiel Lavezzi's half-volley over the bar, but Sabella was left to reflect on a below-par performance in Argentina's final friendly before he names his World Cup squad.