Reading opened the scoring through centre-back Scott Dann, heading in from a John Swift free-kick, before Tom Dele-Bashiru finished calmly to put the home side two up.
But it was Yates again who gave the Tangerines the lead, converting from the penalty spot after Sonny Carey was brought down in the box to take all three points back to Lancashire.
This result takes Blackpool up to 12th in the table, while Reading drop one place to eighth.
Story of the match
After a fairly even opening ten minutes, Reading opened the scoring through veteran centre-back Dann. He nodded in a free-kick from Swift to give the hosts the lead and score his first goal for the club since joining at the end of August.
After the goal, Blackpool started to push on to get an equaliser and almost got one. Jordan Gabriel hit an effort from the edge of the box which was parried by Southwood, only for him to perform some quick reflexes to save the follow up from Yates.
Despite Blackpool's pressure, it was Reading who scored again to double their lead. Marvin Ekpiteta was dispossessed by George Puscas, who fed Josh Laurent in on goal. Laurent was unselfish by playing it on for Dele-Bashiru, who proceeded to smash it in from six yards.
Blackpool continued to press on as they looked for a way back into the game, but Reading continued to defend valiantly. Blackpool's best chance was through a counter-attack, in which Keshi Anderson was put through on goal. Unfortunately for Blackpool however, the attacker took too long to pull the trigger causing a brilliant block from captain Liam Moore to stop what would have been a certain goal before half time.
The Royals started out the second half the better of the two sides, with Puscas close to ending his goal drought when he was put through on goal, only for his shot to be saved.
A quiet second half was brought to life however when the Tangerines got back in it with 20 minutes to go. Dale, who came on for his debut just five minutes prior, smashed it in from the edge of the box after it was cleared from a corner to half the deficit.
Four minutes later and Reading waved goodbye to their lead, when an unmarked Yates got his head on a cross from the left-hand side to make it 2-2.
With just over five minutes to go, Blackpool got their winner, with the away side winning a penalty through Carey, when he was brought down in the area. Yates stepped up and converted it to finish the away sides comeback.
Man of the match
The frontman was clinical for the away side tonight, scoring two goals, with a fine header and a calm finish from the penalty spot to help his side come away with all three points.