The 22-year-old lit up Wearside with the cheekiest of finishes to establish a 2-0 lead for his side at the Stadium of Light when he backheeled his 51st-minute shot past goalkeeper Simon Mignolet as he came from his line.
But, having opted for the outrageous, Sturridge was forced to look on as the ball dribbled agonisingly towards the bottom corner with defender Brown in hot pursuit.
However, the former Manchester United man failed to get there in time, much to the striker's relief as his audacity paid off and he avoided a dressing down for not taking a more conventional approach.
Sturridge told BBC Sport: "I was hoping he wouldn't get it and I was thinking, 'Oh God, he's got it'.
"It was a huge moment for it to actually hit the back of the net because I thought he was going to clear it, so I am very happy."
Sturridge's chance to enhance his blossoming reputation came from a superb Raul Meireles through-ball as Chelsea turned in a powerful display to ease their way to a 2-1 victory which was far more comfortable than the scoreline suggested.
He said: "It was a great ball from Raul Meireles, great vision from him. I got across the centre-half and saw the keeper coming out, so I went for a little cheeky one and it paid off."
Sturridge's contribution effectively wrapped up the points after skipper John Terry had fired the visitors in front with 18 minutes gone.
The central defender's strike, which flew in off Sunderland's Phil Bardsley, came six minutes after debutant Nicklas Bendtner had glanced a Sebastian Larsson free-kick just wide at the other end.
But the traffic was largely one way before the break with Nicolas Anelka, preferred to Fernando Torres in attack, and Juan Mata repeatedly stretching the home defence.
Indeed, Bardsley could yet find himself in hot water for what appeared to be a stamp on Mata which went unnoticed by referee Lee Probert as the Black Cats battled desperately to stem the tide.
Having reached half-time just one goal behind, Steve Bruce's men returned determined to drag themselves back into the game, but Sturridge's party piece ensured that substitute Ji Dong-won's first goal in English football, which arrived in injury time, counted for little.
Chelsea boss Andre Villa-Boas was a happy man after seeing his side reproduce their training ground work on the pitch for the first time this season, significantly without £50million man Torres until the final 16 minutes.
However, he insisted the Spaniard's absence from the starting line-up was indicative of nothing other than Anelka's form and freshness.
He said: "I have four wonderful strikers and all of them compete highly for the forward positions.
"All of them offer different kinds of things because they have different talents, and today [Saturday] the choice fell to Anelka."
But while one manager was happy juggling his frontmen, the other was contemplating life without his record signing.
In a shock development in the Asamoah Gyan saga, which had been rumbling below the surface for months, it emerged shortly before kick-off that the Ghana international was to join United Arab Emirates side Al-Ain on a season-long loan deal.
Bruce was scathing in his response after believing the air had been cleared during talks on Thursday.
He said: "I don't want anybody to hang around the place when they don't want to. It's been ongoing now for weeks and months.
"But it sums it up - for somebody to go and leave the Premier League to play in the United Arab Emirates, I can let everyone draw their own conclusions from that.
"Connor [Wickham] and Ji, it's time for them now. I wanted to try to ease them in if I could because they are both so young.
"They will have to come in quicker than I thought they would do, it's as simple as that."
Bruce was at least able to take some consolation on a difficult day from Bendtner's first appearance in a red and white shirt.
The Denmark international found himself engaged in a physical encounter with Terry, but gave as good as he got despite a lack of genuine service, and it was he who set up Ji for his consolation strike amid a late flurry.
Bendtner said: "We seemed to put them under pressure and deservedly, we also got a goal.
"Unfortunately, it was a bit too late, but it is always difficult playing against Chelsea."