The finalists of the Champions League won 2-0 in injury time after goals from Francesco Pio Esposito and Alessandro Bastoni, while the Argentinian outfit was up to nine men after they had seen Lucas Martinez Quarta and Gonzalo Montiel in the second half.
Montiel was sent a few minutes after Bastoni's injury time stunner.
And Acuna looked to take his frustrations on Dumfries after the Dutchman had left a tough challenge just a few seconds.
Dumfries did not let the accusations come to him and even gave something back, but when the full -time whistle of referee Ilgiz Tantashev came, it started again.
While 29-year-old Van de Veld on Lumen Field jogged in Seattle, he was chased by the 33-year-old Acuna while he came in a shower of rockets from the river supporters.
Players from both parties rushed to the corner of the field to get into the middle of the couple, with both River Subs and Interhoofdcoach Cristian Chivu included in a group that held Acuna back before struggling him on the ground.
The result confirmed the progression of Inter to the last 16 as group leaders, who set them up for a delicious draw against colleague South American Club, Fluminese.
In the meantime, River was sent from the tournament after completing a point behind the Mexican outfit Monterrey, who fought his way to two draws against Inter and River before he hit Japanese giant Urawa Reds 4-0.