Joe Mattock's bundled 90th minute equaliser robbed the Royals of a victory they deserved on a horrible wintery day in south Yorkshire.
Caretaker boss Scott Marshall named young defender Tom McIntyre in his back four - the centre-half becoming the club's 48th Academy graduate to break into the first team. Gabriel Osho came onto the bench to take our Academy graduate number to five in the squad of 18, while Dave Edwards and Jon Dadi Bodvarsson were among the substitutes following injury absences.
An early chance fell Reading's way when Yiadom delivered a tasty cross into the box where Baldock directed a header just over the crossbar from 10 yards out.
The hosts' first opportunity came with seven minutes gone - Blackett's clearance dropping for Anthony Forde whose drilled effort skidded wide of the bottom right corner.
But the Royals took the lead two minutes later. Sims cut inside off the right flank and threaded a lovely ball between the defenders to allow Baldock to race into the box having sprung the Millers' offside trap. From a tight angle, he arrowed a shot at goal and Marek Rodak couldn't keep it out.
The Royals were looking good in the final third and Swift's marauding run down the middle ended with a dragged right-footed effort that bobbled agonisingly wide of the Rotherham goal.
Sims was enjoying some space on the right and he was barged to ground as he looked to cut a cross back midway through the half - half-hearted appeals for a penalty were swiftly dismissed by the referee.
United were being restricted to shots from outside the box and Will Vaulks drove an effort wide of the post with Jaakkola covering well. But Sims and then McCleary saw low cut backs cut out before they could reach a Reading body in the middle as Scott Marshall's men sought a second.
With 12 minutes of the half remaining, it should have been 2-0. A brilliant counter attack down the right saw McCleary feed Swift in space. His low cross was anticipated well by Baldock who got in front of his man but turned his effort over the bar from eight yards out.
Then a superb save from Rodak denied the Royals a second. A wonderful exchange between Swift and Baldock saw the former aim an effort at goal but the Rotherham stopper parried it well and another glorious chance passed the visitors by.
Reading continued to press for a second and Swift's aerial ball over the top nearly found Baldock's run in behind - but Rodak was off his line to gather the ball in from the toes of the Royals striker.
And in the first of two minutes of injury time, McCleary was the recipient of an early ball on the counter attack. He has the space to attack the last defender but instead checked back and turned onto his right boot to arc a lovely effort towards the right corner - Rodak again to Rotherham's rescue to palm it away.
Half-time | Rotherham 0-1 Reading
The home side made a double change at the break; Paul Warne appreciating that his side needed to do something different to threaten the Royals' lead.
And Richie Towell tested Jaakkola when his deflected drive needed parrying by the Finnish international.
A combination of Semi Ajayi and Andy Yiadom bundled a dangerous cross behind for a corner as United piled on the pressure with aerial balls and long throws.
Andy Yiadom relieved some of the pressure by forcing Rodak into a fine save high to his right - the full-back letting rip with a fine effort from the edge of the box.
Then minutes later, Swift found a way to the byline on the right and cut a low cross into the near post where Sims met it and turned it against the base of the right upright.
The game was still in the balance and Jaakkola showed superb handling to cling onto a sweetly struck effort from Vaulks with 20 minutes remaining.
The Royals stopper was down low to save a low fizzing effort from Proctor as Rotherham continued to put pressure on a Royals defence trying to combat an aerial attack in the face of falling freezing rain.
Reading still sought a second goal and Bodvarsson was introduced with a quarter of an hour remaining. And Bacuna drilled a left-footed effort inches wide of the left post with nine minutes left on the clock.
United were throwing everything at the Royals back line and it took a goalline clearance from Yiadom to preserve the visitors' lead with six minutes remaining.
And in the 90th minute, the Millers' pressure finally told when Joe Mattock scrappily bundled the ball over the line from an inswinging corner that the Royals failed to clear.
Both teams battled for a winner in five minutes of injury time. And McCleary came close when his show was charged down with a sliding defensive block deep into injury time. And the spoile were shared.
Full-time | Rotherham 1-1 Reading
Rotherham United: Rodak, Vyner, Mattock, Vaulks, Ajayi, Wood (c) (Robertson HT), Forde, Taylor (Newell 68), Towell, Williams (Proctor HT), Smith.
Unused subs: Price, Palmer, Proctor, Robertson, Manning, Wiles.
Goals: Mattock 90
Reading: Jaakkola, Gunter, Yiadom, McIntyre, Blackett, Bacuna (c), Rinomhota, Swift, Sims (Loader 86), McCleary, Baldock (Bodvarsson 79).
Unused subs: Mannone, Osho, Kelly, Edwards, Barrow.
Yellow: Sims, Jaakkola
Goals: Baldock 9
Referee: Mr R Joyce
Attendance: 8,775 (433 away)