All the goals came in the second half with the fourth, scored by substitute Gabriel Jesus one minute after coming on, highlighting Arsenal's depth and coach Mikel Arteta jubilantly high-fived his assistants at Tuesday night's final whistle.
Victory moved Arsenal five points ahead of Manchester City, who play at Sunderland on New Year's Day, and six points clear of third-placed Villa.
Elsewhere, Chelsea drew 2-2 at home to Bournemouth; Newcastle won 3-1 at lowly Burnley; and Manchester United were held 1-1 at home to rock-bottom Wolverhampton.
Struggling West Ham drew 2-2 with visiting Brighton, and Everton won 2-0 at Nottingham Forest.
Arsenal have not won the Premier League since 2004 and the pressure is on Arteta to deliver.
"In 2026, we know what we want," Arteta said.
No Arsenal player is near the top of the scorers' charts this season, yet sharing the goals around might just be the team's strength.
Defender Gabriel Magalhães headed home early in the second half following a corner for set-piece specialist Arsenal, and midfielder Martín Zubimendi netted in the 52nd minute.
Winger Leandro Trossard curled in a fine third from the edge of the penalty area in the 69th and was involved in the fourth goal, curled into the same corner from almost the same spot in the 78th minute by Jesus after Arsenal launched a superb counterattack from deep.
The win was even more impressive considering Arsenal were missing key midfielder Declan Rice with a knee injury and Villa were playing on the back of 11 straight victories in all competitions.
Gabriel nodded in from close range, deemed not to have impeded Villa goalkeeper Emiliano Martínez with his elbow.
Zubimendi finished after captain Martin Ødegaard expertly won the ball in midfield and advanced before threading a perfect ball behind Villa's defence.
Ollie Watkins grabbed an injury-time consolation for Villa.
Bournemouth's David Brooks netted early from close range after Chelsea failed to deal with a throw-in.
Cole Palmer equalised in the 15th with a penalty awarded after a video review ruled that Antoine Semenyo's knee had gone into the back of Estevão's leg.
Enzo Fernández gave Chelsea the lead midway through the first half, but Chelsea gifted Bournemouth an equaliser when a defender headed on a throw-in and Justin Kluivert scored at the back post for 2-2.
Chelsea are fifth and level on 30 points with United in sixth.
Manchester United led through Joshua Zirkzee's deflected strike in the 27th but Ladislav Krejčí equalised close to halftime for Wolves with a header.
It was Wolves manager Rob Edwards' first point since taking charge in November.
Yoane Wissa grabbed his first league goal since joining from Brentford as Newcastle moved into 10th spot.
Newcastle were 2-0 up inside seven minutes with Joelinton being set up by Anthony Gordon and Wissa bundling in following a goalmouth scramble.
Josh Laurent pulled a goal back for Burnley midway through the first half. Newcastle survived nervy moments before Bruno Guimarães sealed the win with a lob in stoppage time.
Next-to-last Burnley are two points behind West Ham in 18th.
Everton netted in the 19th when James Garner drilled in a low finish after being set up by Dwight McNeil.
Garner then turned neatly in midfield before feeding Thierno Barry to make it 2-0 against Forest in the 79th.
West Ham took an early lead against Brighton when striker Jarrod Bowen latched onto Lucas Paquetá's through ball from halfway and struck a low shot into the bottom corner.
Veteran forward Danny Welbeck equalised for Brighton from the penalty spot and then hit the crossbar with a Panenka-style chipped penalty later in the first half.
Paquetá converted his spot kick in first-half injury time, but Joël Veltman equalised for Brighton in the 61st following a corner.
Defending champions Liverpool host Leeds on Thursday.
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