Bardsley did get one back for the hosts, but it wasn't enough.
Here, Sports Mole takes a closer look at the events that unfolded.
On target 3
On target 5
Was the result fair?
After going a goal up, Sunderland failed to build on their good start and allowed Chelsea back into the match. They gave danger players like Eden Hazard and Juan Mata too much space, and Hazard exploited that with a sublime display of skill and precision. At the end of the day, he was too much for the Black Cats to handle, but they can be proud of their performance.
Gus Poyet will be pleased with how his players started the game, grabbing an early goal and defending well. They weren't outplayed by their opponents, and Poyet might argue that without Hazard, the result could have been different. Nevertheless, Sunderland look capable of avoiding relegation.
Jose Mourinho's men were not at their best defensively, but they made up for that with their attacking play. Hazard, Mata and Willian looked dangerous every time they went forward, although Fernando Torres was poor. Mourinho will be happy that Chelsea look capable of scoring plenty of goals, but he might want his defence to tighten up a bit.
Sports Mole's man of the match
Eden Hazard: The Belgian was at the height of his powers tonight, injecting the game with a dose of real quality. He scored two, both of which were magnificent, and provided the assist for Lampard's header.
With the game in the balance at 2-2, Torres had a glorious chance to put Chelsea ahead, but blasted his shot over the bar when it looked easier to score. A bad miss on a disappointing night for the striker. Bardsley's own goal was unfortunate, but he was trying to clear the ball.
Phil Dowd had a decent game with the whistle. However, he could have given a penalty when Demba Ba appeared to be pulled back, and Jack Colback might have been sent off for tugging at a shirt shortly after he had been booked.
Sunderland: Poyet's men have a home match against Tottenham Hotspur on Saturday.
Chelsea: Chelsea travel to Stoke City on Saturday afternoon.