Dave Kitson's superb second-half strike earned 10-man Reading only their third away point of the season at Upton Park.
Solano's fine finish was more than matched by Kitson's strike
The visitors looked more threatening until Brynjar Gunnarsson saw red for a two-footed lunge at Hayden Mullins.
Nolberto Solano dinked West Ham ahead and Marcus Hahnemann denied Scott Parker but Kitson latched on to Nicky Shorey's pass to fire home expertly.
Jonathan Spector and Dean Ashton hit the woodwork as West Ham pressed in the closing stages but Reading hung on.
It was no more than they deserved for playing a full part in an entertaining clash which belied the teams' poor records - West Ham were searching for only their third home win and the Royals their first victory away from the Madejski Stadium.
There were plenty of efforts on goal in a bright opening - albeit lacking the direction or power to seriously inconvenience the keepers.
Ashton played in Mullins, who shot straight at Hahnemann, and the powerful striker was brought down by Ivar Ingimarsson for a free-kick which Solano curled just wide.
After those opening forays from the hosts, Reading posed the greater threat on the break, particularly through Bobby Convey and Stephen Hunt down the flanks.
The lively Kevin Doyle and Kitson combined to leave Convey in front of Robert Green inside the six-yard box, only for the keeper to bravely deny the American winger.
Ashton went close soon after with a dinked shot which looped just over the bar with Hahnemann beaten.
And once Gunnarsson was dismissed, Carlton Cole's persistence led to the ball breaking for Solano, who ran through to clip the ball over and across the on-rushing Hahnemann in the 42nd minute.
It was pretty much one-way traffic at the start of the second half, with West Ham making their numerical superiority count.
Reading dug out a point after Gunnarsson's first-half dismissal
Hahnemann bravely denied Parker after the midfielder unleashed a powerful shot from an acute angle.
But Reading refused to buckle under the pressure and stunned the home crowd with a brilliantly worked equaliser on the hour-mark.
The impressive Shorey chipped through a pass which the swivelling Kitson pounced on to fire beyond Green.
With the game now stretched, West Ham twice went desperately close to regaining their lead.
Spector headed against the angle of post and bar and Hahnemann majestically palmed away Freddie Ljungberg's strike after Parker had picked him out.
The Hammers also had claims for a penalty waved away in the closing minutes when Mark Noble's cross appeared to brush Ingimarsson's hand.
And Ashton hit the post with a header right at the end of a hard-fought encounter which, just about, ended with the right result.
West Ham manager Alan Curbishley:
"I'm as frustrated as the fans and players. We couldn't quite get the goal that would have finished the game off - we had a few chances to do that but didn't take them.
"We needed a second goal. We knew Reading would keep going and the goal gave them something to hold on to but we should have finished it.
"We keep setting our fans up by winning away and then coming back here and not doing it but it is not for the want of trying."
Reading boss Steve Coppell:
"We were disrupted by the sending-off but we got through to half-time and we had to be very careful how we approached the second half, in terms of commitment and trying to salvage the game.
"We thought if we could keep it tight for the last 15-20 minutes it would be interesting - we knew we would get oppportunities.
"It was terrific play from Shorey and Kitson and it fell to the right man. He was very sharp in finishing it off."
West Ham: Green, Neill, Spector, Upson, McCartney, Solano (Noble 77), Parker, Mullins, Ljungberg, Cole (Camara 72), Ashton.
Subs Not Used: Wright, Ferdinand, Pantsil.
Booked: Green, Cole.
Goals: Solano 42.
Reading: Hahnemann, Murty, Sonko, Gunnarsson, Shorey, Hunt, Harper, Ingimarsson, Convey (Cisse 66), Doyle (Bikey 90), Kitson (Long 85).
Subs Not Used: Federici, Lita.
Sent Off: Gunnarsson (29).
Booked: Hunt, Shorey.
Goals: Kitson 60.
Ref: Peter Walton (Northamptonshire).
BBC Sport Player Rater man of the match: Nolberto Solano 8.06 (on 90 minutes).
Please note that you can still give the players marks out of 10 on BBC Sport's Player Rater after the match has finished.