Darren Pratley's first-half header put Wanderers into a half-time lead at the Reebok Stadium.
But David Wheater's handball in the early stages of the second half saw Blackman level from the spot, ensuring both sides maintain their unbeaten starts to the season.
Jay Spearing, signed 24 hours before kick-off from Liverpool, went straight into Dougie Freedman's starting 11 for the hosts.
The Trotters carved out the first opportunity. Jermaine Beckford went through a clutch of defenders and looked to be through on goal but for Danny Guthrie's cynical challenge, which earned the former Newcastle midfielder a booking.
With 14 minutes gone the home side took the lead, Marc Tierney's inswinging cross falling perfectly to Pratley, who headed the ball back across Alex McCarthy and into the left corner of the net.
Guthrie had the chance to equalise from near the penalty spot but could not keep his shot from a Royston Drenthe pass on target.
Bolton almost doubled their advantage five minutes before the break. Medo Kamara took a chance from 35 yards out, his thunderous strike beating McCarthy but slamming against the right-hand post.
Wheater's error then gave Reading the chance to level, Jobi McAnuff's corner hitting the centre-half's hand and the assistant referee awarded the spot-kick.
Blackman stepped up and made no mistake, side-footing past Adam Bogdan in the 51st minute.
The goal gave the visitors a huge spark, and, if not for the heroics of Bogdan, they could have taken the lead, with Drenthe's long-range effort and then Alex Pearce's header from the edge of the six-yard box both kept out by the Trotters stopper.
Bolton then had a penalty shout of their own, with Pratley's corner appearing to strike Wayne Bridge's arm, but the claims were waved away by referee Carl Boyeson.
Reading broke to good effect as McAnuff and Drenthe combined to put Adam Le Fondre one-on-one with Bogdan but the striker failed to convert.
Bolton's Alex Baptiste then walked a tightrope as the former Blackpool defender looked to have taken down Drenthe and later McCleary in the penalty area. However, neither was penalised but Drenthe did receive a yellow card for diving.
Bogdan came to the rescue again late on, saving Sean Morrison's header from point-blank range to make sure Bolton continued their 12-match unbeaten record at home.