Barba gave the Bulldogs a fifth-minute lead before Canterbury five-eighth Josh Reynolds made the Warriors pay for a turnover in the 13th minute to make it 12-0. And it was 16-0 a few minutes later, when Barber showed far too much speed for Jermone Ropati on the right wing before feeding Jonathan Wright on the inside.
At that point, the Warriors were yet to have an attacking set inside the Bulldogs' red zone, with the visitors' advantage reflected in the tacking statistics. At the mid-point of the half, the Warriors had made 80 tackles to the Bulldogs' 33, while the hosts had also missed 10 tackles.
But that all began to change in the last 15 minutes of the opening half. A big hit by Manu Vatuvei on Josh Morris gave the Warriors their first chance to attack Canterbury's line and, although that chance was squandered, the tackle seemed to turn the tide of the match.
First, Konrad Hurrell thought he had put his team on the board but the video referee had other ideas, before Feleti Mateo came off the bench to put the Warriors back in the match.
A clever pass in midfield put James Maloney clean through, and the five-eighth showed great speed and strength to pull the Warriors to within 10. Mateo then repeated the dose the very next set, as Sione Lousi crashed through close to the line to leave the Warriors trailing by 16-12 at the break.
The Warriors drew first blood in the second spell and, again, it was Mateo making the difference, selling a dummy down the left hand side before squeezing through two tacklers and over the line.
Maloney's conversion gave the Warriors their first lead of the match but that lead lasted fewer than 10 minutes. Auckland-born Sam Kasiano looked to be well and truly wrapped up close to the line, but the prop somehow managed to force the ball over the line despite the attention of four defenders.
With 10 minutes remaining, another moment of Mateo magic appeared to again put the Warriors ahead. A superb inside ball sent Kevin Locke through and the fullback went over in the corner, but the video referee ruled a tackle from Barba forced Locke across the sideline.
Barba then backed up his try-saving heroics with a break which sealed the game, with the Bulldogs spreading the ball to the left side where Wright crossed to continue the Bulldogs' perfect start, before Joel Romelo added gloss to the win.
Warriors 18 (Maloney, Lousi, Mateo tries; Maloney 3 cons)
Bulldogs 32 (Barba, Turner, Wright 2, Kasiano, Romelo tries; Turner 4 cons)
HT: 12-16