The England left-back was recalled to the starting line-up as Alexis Sanchez scored a brace to see off the spirited Tigers at the Emirates Stadium with Arsene Wenger's side picking up three vital points following two successive defeats.
Sanchez opened the scoring with a contentious close-range effort that went in off his hand and led to referee Mark Clattenburg apologising to Hull's players for missing the infringement.
The Chilean completed the scoring as he secured a 2-0 win with a last-gasp penalty after Hull had seen Sam Clucas dismissed for clearing Lucas Perez's shot off the line with his arm.
The victory not only keeps Arsenal's slim title challenge alive but also means they retain their place in the Premier League top four ahead of Wednesday's Champions League tie at Bayern Munich.
But Gibbs, handed his first start since Boxing Day in the only change from the 3-1 reverse at Chelsea, agreed with Wenger's assessment that the hosts played with the "handbrake" on.
"It was a good chance to show a response and we certainly did that," he told Arsenal TV.
"But still at times I thought we could play a lot better. We've got a squad that can cause a lot of damage, so we will tie up those ends - defensively and in the final third - sharpen up and look even stronger.
"It's obviously nice to get a clean sheet as well after a couple of defeats, so we can look forward now."
For Hull and their boss Marco Silva, the game brought to an end a tough run against some of the league's biggest sides.
The Portuguese manager and his players have emerged from facing Chelsea, Manchester United, Liverpool and Arsenal in their last four league games with four points and renewed belief they can survive in the top flight.
Silva, whose side host Burnley in their next outing in a fortnight, now wants his side to build on a number of impressive displays.
"I saw some positive things in the game," he said. "I didn't like the way we started but we reacted and I am happy that the team showed good things again. We caused Arsenal plenty of problems and I want the team to continue with the progress we are making.
"We have time before our next game - time to rest and time to work on things for the next game."
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