Iturbe, dubbed 'Mini Messi' when he earned a place in Argentina's under-20 team as a 16-year-old, had just scored River's third goal in the 87th minute of a 3-1 victory that condemned San Martin to the second division.
With the adulation of the huge crowd at a packed Monumetal still ringing in his ears, Iturbe did some trickery in added time that annoyed the visitors, was fouled and made matters worse by encouraging the fans with arm gestures.
San Martin's players, including some of their bench, went for the stocky 20-year-old, who had to be protected by police.
Referee German Delfino showed Iturbe and four San Martin players the red card as he ended the match, adding to his 68th-minute dismissal of visiting defender Damian Ledesma.
"They all wanted to hit me, even the reserves came charging towards me," Iturbe, set to return to Porto after a six-month loan deal, was quoted on Monday as telling reporters.
"I can understand their situation and if my attitude bothered them, I apologise a thousand times, but I was happy at scoring in my last match," he said.
San Martin coach Ruben Forestello was in conciliatory mood, saying: "We're not going to blame Iturbe (for relegation)."
River, who bounced back from relegation at the end of last season, ended the "Final" championship, second of two in the season, second to Newell's Old Boys.
Their arch-rivals Boca Juniors had one of their worst ever seasons and just managed not to finish bottom of the standings thanks to a 1-1 draw at Godoy Cruz.
Relegation in Argentina is decided on teams' average points over three seasons so it did not catch Boca out but San Martin did go down despite finishing the "Final" in ninth place.
They were the last of three teams to be relegated, including Independiente and Union.