Fabio Borini netted a late penalty on Saturday to end Chelsea's 77-match unbeaten run in Premier League home games under Jose Mourinho and offer a huge boost to Sunderland's bid for top-flight survival.
They remain bottom of the table and three points from safety, but three of their four remaining games are at the Stadium of Light against fellow strugglers Cardiff City, West Brom and Swansea City.
And O'Shea revealed that despite their lowly status, Poyet made it clear to his players before the match at Stamford Bridge that they should be gunning for Mourinho's imperious record.
Interviewed alongside Borini on Sky Sports, O'Shea said: "Have a guess what the manager's team talk was - 'be that team to beat that record. What about, why not?'
"What's the headline going to be in the morning? Mourinho loses his record.
"The manager has always deserved a lot of credit and this man (Borini), if there was a cooler man in the stadium when he stepped up to take that penalty ... he was different class."
When asked what was going through his mind when he approached the spot eight minutes from time, Borini simply replied: "Goal. That's why you take penalties because you're confident and you normally see a goal.
"That's the only solution you have to take penalties.
"We're up for the relegation battle and we showed that we have great character and great belief in this target."
Connor Wickham followed up his midweek double in the 2-2 draw at Manchester City by cancelling out Samuel Eto'o's opener for the hosts.
It was left to fellow forward Borini to add a further twist to the title race, and the Liverpool loanee was happy to answer the pre-match wishes of fans from his parent club, who will take a five-point lead at the top of the table with victory over Norwich City tomorrow.
He added: "I had lots of tweets from Liverpool fans asking a favour and it's not only for them. It's more for us, for Sunderland."
