The Blues were strongly backed to beat Arteta's side on Boxing Day, with Arsenal only four points clear of the relegation zone at the start of the day.
But Alexandre Lacazette, Granit Xhaka and Bukayo Saka all scored to secure the Gunners a convincing win over their well below par opponents and move six points clear of the bottom three.
Lacazette and Xhaka both netted in the first-half before Saka grabbed his goal after the break, with Tammy Abraham scoring a late consolation for Chelsea and Jorginho missing a penalty.
Up next for Arsenal is a trip to Brighton on Tuesday evening, and Arteta hopes Saturday's victory is the start of something big - rather than just a one-off derby day win.
"It's really big for everybody," Arteta told talkSPORT. "The most important for me is for the team, because a team that is doing a lot of things right but is not winning football matches means you cannot build any belief or consistency because you need the points at the end of the day.
"In the Premier League over the last few weeks a lot of things have happened which means we haven't picked up enough points.
"This is what we needed. Hopefully this will give us more confidence so we can pick up results and grind wins.
"But it's going to be really challenging because recovery times are minimal between every game in the Premier League.
"But it's good to win today."
Arteta sprung a few surprises when his line-up was confirmed, with youngsters Gabriel Martinelli and Emile Smith Rowe both included in the starting XI.
But it's fair to say it was a brilliant decision by Arteta as both starlets impressed, along with the 19-year-old Saka who scored the third goal at the Emirates.
"We chose to give them an opportunity because we had some big senior players on the bench, and they deserved the chance," explained Arteta. "They have been training really well and we needed their energy today, and I believed they could give us something different."
Mikel Arteta hopes Arsenal's unexpected defeat of Chelsea is the catalyst for the Gunners picking up some much-needed points to move up the Premier League table.