River have 32 points with two matches remaining in the 'Final' championship, equal with Newell's Old Boys, who can pull away again if they do not lose to relegated Union at home in Rosario on Monday.
Argentina under-20 international Iturbe, dubbed the new Lionel Messi and nicknamed "Little Flea" when he emerged as a 16-year-old, put River ahead midway through the first half from fellow striker Rogelio Funes Mori's square pass in the box.
River went two up after an hour when Iturbe, who is on loan from Porto, beat left-back Lucas Villalba for speed on the right and crossed low for midfielder Manuel Lanzini to fire past Diego Rodriguez in the Independiente goal.
Independiente fans reacted badly to the second goal, tearing up seats in the top tier behind one of the goals at River's Monumental stadium and hurling them down on to River supporters below. There were no reports of any injuries.
The visitors pulled a goal back through playmaker Daniel Montenegro in the final minute but they now depend on a defeat for Argentinos Juniors at San Lorenzo on Monday to avoid being relegated for the first time.
The record seven-times South American champions are in the bottom three of the relegation standings, a separate table with teams' average points over three seasons.
The bottom three go down at the end of the season on June 23 and Independiente must win their last two matches at home to San Lorenzo and away to Colon in Santa Fe to stand a chance of surviving in the top flight.
Independiente coach Miguel Angel Brindisi tried to pour cold water on his team's impending doom by referring to River's traumatic relegation in June 2011.
"Two years ago, in this place there was a tragedy. The same players came back and today have the honour of playing for the championship," Brindisi said.
River bounced right back as second-tier Primera B Nacional champions last year, although a majority of the squad now fighting for the first division title were signed after promotion.
"The defeat complicates things much more... there's a large margin of risk and our chances have got smaller but our heads won't drop," added Brindisi, who took charge in mid-April and has picked up 12 points in eight games.
