Victory took the Gunners nine points clear at the top of the Premier League as they chase a first English title in 22 years.
Martin Zubimendi's fine strike broke the deadlock just before half-time at the Emirates before Gyokeres sealed victory in the second half.
The Sweden international lashed home a shot from Kai Havertz's pass before Gabriel Martinelli teed him up to slot into an empty net in stoppage time.
Gyokeres has struggled to match his prolific form at Sporting Lisbon, which earned him a £64 million move to Arsenal.
But he is Arteta's top scorer with 13 goals in all competitions, including six in his last eight appearances.
"Confidence is the magic word. When you feel confident, when you feel important, when you feel at your best, that's when you can really take your game to the highest level," said Arteta.
"We are really behind him in every moment to try to help him, to try to support him. He is delivering, and he's in a really good moment now.
"Obviously, when you put that shirt on, there is lot of responsibility and huge expectation, and you need to live with that."
Manchester City can reduce the gap at the top back to six points on Sunday, but will need to secure their first win away to Liverpool in front of a crowd since 2003 to do so.
Arteta said he will be watching the clash between the two sides that have dominated English football over the past decade, but insisted Arsenal still have plenty of work to do to deliver a long-awaited title.
"We still have to win so many games to achieve what we want," added the Spaniard.
"I'm going to have a beautiful dinner tonight. Tomorrow I start to prepare for Brentford (on Thursday), because it's going to be a really tough one.
"And in the meantime, I will be watching a big, big game."