Captain Lionel Messi curled in a corner in the 67th minute and Otamendi, unmarked at the near post, nodded the ball down and into the net before rushing off to lift the Barcelona playmaker.
Messi orchestrated most of the attacks but Argentina found it tough to beat Venezuela keeper Rafael Romo at the Yuba Bharati Stadium.
Romo made several saves including one brilliant effort to foil Messi that led to the 67th-minute corner.
Javier Pastore could have made it 2-0 after Romo collided with Gonzalo Higuain but the substitute blasted the ball over an empty net.
Earlier, Venezuela created the first real chance of the game only to see Jose Rondon squander his opportunity.
Rondon's team mounted several attacks in the first half without having a single shot on target.
DRIBBLING SKILLS
Messi showed off his dribbling skills when he evaded three challenges to set up Angel di Maria inside the box but the Real Madrid player shot wide.
Argentine Messi later beat two defenders in the box before unleashing a tame shot that Romo had no problem gathering.
Sabella took over as coach after Sergio Batista failed to guide the former world champions beyond the quarter-finals of the Copa America in July.
Kolkata is renowned for its football passion and a local derby featuring East Bengal and Mohun Bagan often draws a crowd in excess of 100,000.
The former capital of British India has previously hosted greats like Pele and Diego Maradona but this is the first time the eastern city has hosted such a high-profile match.
The game was staged by a local event management company.
