Argentina -- who are grouped with Iran, debutants Bosnia-Herzegovina and African champions Nigeria in Brazil -- were hindered by a clearly under the weather Messi, who played the whole of the match despite being physically sick seven minutes in.
Argentinian coach Alejandro Sabella started with mainly his first choice side with Messi in the playmaking role while Sergio Aguero and Gonzalo Higuain were the strikeforce and other regulars such as Angel di Maria, Javier Mascherano and Pablo Zabaleta also featured.
With Messi not at his best, little of note was created in a first-half which saw few chances for either side.
However, Romanian midfielder Alexandre Maxim should have done better when he was found unmarked in the 33rd minute but he aimed his downward header straight at Monaco 'keeper Sergio Romero who kept it out with his legs.
The Romanian midfielder thought he had atoned for that miss when he fired home into the far corner five minutes later but the linesman ruled that the ball had gone out when it was crossed into the box.
The visitors had their best chance of the first-half a minute later as a piece of individual magic from Aguero saw him slip past two defenders and into the box only to miss the target.
Maxim was withdrawn at half-time -- one of two Romanian changes -- while Sabella kept his side unchanged with Messi seemingly recovered.
Aguero had an early chance in the second-half as he slipped free of the home defence but he took the ball too wide and his shot was cleared for a corner which was the last piece of notable action for him as he was taken off and replaced by Rodrigo Palacio.
Messi was still not 100 per cent and it was left to others to trouble the Romanians with Zabaleta and Palacios combining in the 65th minute to set up Higuain but his shot shaved the post.
The ponderous Palacios was at fault for a terrible miss with 20 minutes remaining.
Di Maria got free on the left and found Palacios five yards out but he stumbled over the ball and saw it drift wide.
Di Maria also let a golden opportunity go abegging as Zabaleta found him with a brilliant 60 yard ball but his volley went high over the bar.
Argentina nearly won it five minutes from time as Messi chipped over the defence to find Palacios who then sent over a teasing cross but Higuain's volley was tipped over the bar.