Millwall moved up to third spot in the Championship table, but were left with a sense of frustration at not clinching all three points as The Lions failed to score at home for the first time in 21 games.
Wycombe Wanderers were the last team to leave The Den in a league game with both a clean sheet and victory way back on 21st November 2009 when they capitalised on a below-par Lions performance.
But on this occasion the only thing lacking from Kenny Jackett's men was that final decisive touch in front of goal.
"It was a good performance, we put them under a lot of pressure and created a number of chances," said boss Kenny.
"Reading are a side with quality but I am pleaded with the way we've closed the gap between ourselves and teams like them.
They came here to attack and made it a cracking game, but my players didn't do a lot wrong and were unfortunate not to win."
Jackett made a couple of changes to the side that started against Nottingham Forest on Saturday with Tamika Mkandawire stepping in to partner Jimmy Abdou in central midfield for his full Championship debut, whilst Kevin Lisbie was given the nod ahead of Neil Harris, who dropped to the bench.
Abdou sent a fifth-minute header wide of the mark from close range, but his blushes were saved by the linesman's flag whilst former Royals winger James Henry sent a speculative 30-yarder over the bar.
A smart reverse pass by Scott Barron set Steve Morison free on the left after 15 minutes, and the Welsh international striker's surging run could have paid off with a goal, only for visiting keeper Adam Federici to palm away his effort.
The opening half an hour was a relatively quiet affair but the game really sprung into life when Reading's Jimmy Kebe saw his smart angled finish ruled out, with linesman Mr Bull having already raised his flag for offside.
This was to prove a timely reminder to the home side, and spurred them into an intense 15-minute spell of pressure before the break that so nearly yielded the opening goal.
No-one more than Morison will be left wondering how he hadn't bagged a brace during that period, when he was twice denied brilliantly by the athleticism of Federici.
First, on 36 minutes, Forde's quick throw picked out Danny Schofield, he in turn produced an inch-perfect pass to Morison who powered forward before hitting a crisp effort that seemed to be curling beyond the keeper's reach, only for Federici to somehow touch round the post at full stretch.
Then deep into first-half injury-time Morison burst through the heart of the Royals rearguard in a central position. You would have put your house on him scoring his sixth goal of the season, but Federici again came to the rescue with a fine save.
Millwall maintained the momentum after the break and a sweet passage of play on 48 minutes saw Henry's inviting ball curl a whisker away from the outstretched boot of Morison.
A fizzer from Henry was held at the second attempt by Federici, who was then left scrambling across his goal as Schofield's sweetly-struck effort was deflected for one of seven second-half corners.
At the other end David Forde followed up his fantastic display at Nottingham Forest with a magnificent 'how-on-earth-did-he-manage-that' save to keep out Shane Long's goal-bound header at point-blank range.
Reading, to their credit, did not rest on their laurels and were not content to sit back and settle for a point.
In fact it took another top drawer save by Forde to deny former Lions loanee Jem Karacan 11 minutes from time, with the big Irish stopper flinging himself low to his right to push the midfielder's 20-yard bullet onto the foot of the post.
Seconds later it was The Lions who were left ruing their luck when Henry's low cross looked to have picked out an unmarked Mkandawire four yards out. Royals defender Matt Mills got the feintest of touches which did just enough to put Mkandawire off his stride and the ball flew agonisingly out of his reach.
Dunne hit a rasping drive a yard over as The Lions tried to grab that all-important opening goal, but no matter how hard they banged on Reading's defensive door, there was to be no way through.
Millwall: Forde, Dunne, Barron, Abdou, Robinson, Ward, Schofield, Mkandawire, Lisbie (Harris, 73mins), Morison, Henry. Subs not used: Mildenhall, Hackett, Craig, Smith, Laird, T.Robinson.
Booking: Robinson (6mins), Morison (88mins)
Reading: Federici, Karacan, Mills, Long, McAnuff, Kebe, Church (Hunt, 74mins), Howard, Harte, Cummings (Antonio, 81mins), Pearce. Subs not used: Williams, Gunnarsson, Khizanishvili, Robson-Kanu, McCarthy.
Bookings: Long (13mins), Harte (32mins), Kebe (73mins)
Ref: DJ Phillips
Att: 11,061 (away 816)