The visitors had struck first inside five minutes to lead through Nicolo Barella, before a Milan Skriniar own goal had brought their hosts back into the game.
Both teams looked set to settle for a share of the spoils, but Bijol’s powerful glance off Gerard Deulofeu’s corner followed by Arslan’s sharp header in injury time sealed the points for Udinese.
Defeat means Simone Inzaghi’s side will return in October facing a fight to get back into the top four, with the result moving Udinese top ahead of Milan’s clash with Napoli and Atalanta’s trip to Roma.
A brisk end-to-end opening saw Inter seize the early advantage, with Barella steering a sublime free-kick into the top-left corner from 20 yards out.
Udinese were unfazed, though, and when Skriniar turned Roberto Pereyra’s free-kick past his own goalkeeper, parity was restored.
Ten minutes into the second half, Edin Dzeko thought he had put Inter on top again, only to be flagged for offside after turning Barella’s ball into the back of the net.
That let-off emboldened Udinese, who exerted pressure on Samir Handanovic’s goal and were rewarded when Bijol escaped his marker to complete the turnaround.
Inter’s late push for an equaliser did not bear fruit, and Arslan’s close-range finish was the signal for pandemonium among the home support, as Udinese’s excellent start to the campaign continues.