The Black Cats entered the encounter under considerable pressure, having failed to win any of their previous seven league matches and suffered a 2-0 Europa League defeat to Dinamo Zagreb on Thursday.
Regis Le Bris’ side suffered an early blow when Granit Xhaka was forced off with a calf injury in the fourth minute.
However, Sunderland then took the lead through Enzo Le Fee’s 36th-minute penalty.
The Blues pushed for an equaliser, but the hosts defended well to secure all three points and move off the bottom of the Premier League table.
Speaking to Flashscore in the mixed zone, the 31-year-old revealed what his team did differently against Xabi Alonso’s side.
"I think a lot of it's still trying to stay to what we did last season. Success leaves clues," O'Nien said.
"How were we successful last season to now? What are we not quite doing? The evidence is when we watch the games back. It's really, really clear sometimes.
"So, today we're really, really tight. We're a lot tighter, we're a little bit more aggressive at the same time."
He acknowledged that Sunderland's recent struggles had not necessarily been down to a lack of effort.
"Sometimes all the effort's there and we don't get the result. And then, again, you just have to look at it and go, right, let's try this, let's get better at this, let's keep working individually, collectively," he added.
"You keep doing that, you keep compounding that, again, performances like that happen.
"But, as you said, we've got to do that tomorrow, the day after that, next week, weeks after that. If you keep doing that, then you'll keep getting points."
O'Nien demands consistency
The victory lifted the Black Cats to 18th in the Premier League table, above Manchester United and Crystal Palace.
Asked how Sunderland would avoid complacency in their upcoming matches, O’Nien said: "Well, it's me driving you, you driving me. Everybody keeps driving each other. We don't accept anything below the level that we want.
"Again, losing happens. Performances, mistakes happen. But it's the way we respond, it's the way we train.
"Every pass and drill, every possession, it's demanding the standards and the playing style that we are. We've really turned that up intensely over the last few weeks. Even when we've lost, that intensity has been going there; it just hasn't quite married up yet.
"Because sometimes it takes time just to turn that momentum, and today we did."
Similarly, manager Le Bris praised his players’ intensity and strong connection with the fans, stressing the importance of rediscovering Sunderland’s identity after a demanding run of nine matches.
"The aggression was there, the intensity was there, the energy was there. Three points at the end of it all,” said the Frenchman.
"It was important before the international break, at the end of this nine-game block. The three points are crucial in the league, but also the reconnection with our identity and our fans.
"Every three days you have to reset and go again, but today the connection was perfect.
"The more we play this style of play, the more they support us. It’s like a circle which helps the energy to grow in the stadium and supports the players."
Sunderland will hope to build on this victory when they face Unai Emery’s Aston Villa on November 21, before returning to Europa League action against Jagiellonia.
