A high-tempo affair ended in parity with Turkish top-tier opponents Genclerbirligi in Papendal.
Adi Popa netted a late equaliser for the Royals, who had led since the early stages, but the Turkish side struck what they thought was a winner soon after in a heartily-contested fixture.
Instead, Roy Beerens hit a brilliant equaliser with the last kick of the game - 2-2 it ended.
The Royals were almost ahead with minutes of kick-off - George Evans released Adi Popa down the right, who jinked into space before dinking a cross to Pelle Clement at the back stick - but he was under the header and missed high.
And then after Popa's industry had won a corner, Liam Kelly's delivery was headed narrowly wide by Liam Moore, who had stolen a run.
So when the breakthrough came in the seventh minute, it felt like an injustice. Space was afforded to the Turkish side down their left, and when an initial effort struck the bar via a fingertip stop by Anssi Jaakkola, Milinkovic was placed to strike in a rebound from close range.
In seach of an equalising goal, Kelly played a short corner - it was Clement who received, catching the defence unawares, but there was no blue shirt on the end of his cross.
Dutchman Roy Beerens played a smart pass to find Tyler Blackett overlapping on the left; he couldn't quite dig out the cross for fellow full-back Chris Gunter.
Popa's directness down the right flank was giving the Genclerbirligi defence plenty to think about - receiving a Kelly ball into the channel, he shimmied to the byline and a deflected cross looped up and over the backtracking goalkeeper... just onto the roof of the net.
Jaakkola was increasingly a spectactor as the Royals piled forward in search of an early equaliser; towards the end of the first period, he show great alertness and positions to pull off an acrobatic stop. He wasn't to know that the offside flag would be raised.
With the last action of the first half, Kelly stepped up to fire a free-kick after Popa had drawn a foul just outside the area, but the low strike was a yard wide.
While it had been a pulsating first period, the second half began in a more agricultural fashion - both teams showing willing but struggling to break through the defence.
Omar Richards was introduced on the hour, featuring for the second time of the day after playing the closing stages against Kortrijk earlier.
Moore, who led the Championship's block-making tally last season, showed the same kind of defensive awareness as he arrived just in time to hack off the line after the Royals had allowed possession to be turned over upfield.
A raking ball from Beerens sought out the run of Popa through the centre, but he was shouldered out by a covering defender as he tried to trap in the box.
Finally, in the last 10 minutes, the equaliser came. Blackett picked up outside the area, struck sumptuously... the goalkeeper spilled against the post, allowing Popa to follow in from close range.
But parity was short-lived - the Turkish outfit were back ahead when an initial smart stop by Jaakkola wasn't enough to prevent the pieces being picked up and finished in a crowded area.
Blackett tried to force an equaliser as he rose to meet a header, but the Genclerbirligi defence dealt with the threat.
Popa received in space in the final minute, nad only a sprawling save prevented him from netting his second and forcing the draw.
Instead that privilege fell to Beerens, whose stunning strike made it 2-2 with the final kick!
Full-time: Reading 2-2 Genclerbirligi
Reading: Jaakkola, Gunter (c), Blackett, Ilori, Moore, Van den Berg, Evans, Kelly, Beerens, Clement (Richards 59), Popa.