Monreal's opening goal arrived after Alexandre Lacazette was denied by the post during the early stages for Arsene Wenger's side, although Solly March was similarly close to a Brighton equaliser before half-time.
Sanchez took centre stage after the break and set up Iwobi to double the Gunners' advantage with a sublime backheel.
The 28-year-old forward was unable was unable to claim a maiden Premier League goal of the season but his performance offered a vindication of Wenger's hardball transfer window tactics, which left Sanchez unable to complete a deadline-day move to Manchester City.
Lacazette unleashed a rasping 25-yard drive against the post inside two minutes and Arsenal dominated the opening exchanges with pleasingly slick interplay.
Clear-cut chances were not forthcoming, however, and it took a more robust approach to bring about the 16th-minute opener.
1660 - Nacho Monreal has scored his first Premier League goal since 16th March 2013 vs Swansea; 1660 days ago. Cheesy. pic.twitter.com/n4yWPlp1Gh— OptaJoe (@OptaJoe) October 1, 2017
Shkodran Mustafi had an effort blocked following a set piece on the right and Hector Bellerin's follow-up also cannoned into a Brighton body before Monreal rifled in for a first Premier League goal since March 2013.
Brighton had limited opportunities to exert themselves as an attacking force but March rattled the upright when a free-kick was laid into his path after 28 minutes, with Petr Cech helpless. Lewis Dunk was unable to direct his follow-up volley on target.
A scramble in the Arsenal penalty area opened up into a swift counter-attack for the hosts three minutes before the break. Lacazette, Alexis Sanchez, Bellerin and Sead Kolasinac were all involved before Albion goalkeeper Mathew Ryan saved with his boot from Aaron Ramsey.
Sanchez turned in a virtuoso performance after half-time, with his standout moment of brilliance making the points safe in the 56th minute.
35 - Since 2016-17, Alexis Sanchez has been involved in 35 PL goals (24 goals 11 assists), more than double any other Arsenal player. Key. pic.twitter.com/vbcLqkIMc7— OptaJoe (@OptaJoe) October 1, 2017
The Chile star collected Ramsey's pass in the area and moved towards the edge of the box with his back to goal, only to unfurl a delightful backheel.
It meant Iwobi received the ball with ample time to thump into the top corner as the Brighton defence headed off in the wrong direction.
With the result all but settled, the game became a means for Sanchez get the goal his efforts deserved.
He would ultimately be frustrated by Dunk clearing off the line after Ryan took the pace off a 61st-minute effort, while he dragged a later effort wide.
Dunk, who performed tirelessly at the back for Brighton and produced a brilliant recovery tackle on Lacazette, brought down Sanchez at the end of a menacing run, only for the former Barcelona man to swipe the free-kick over.
He pulled his shirt over his face in frustration – an entirely different emotion to that experienced by Wenger and the Arsenal supporters still able to watch Sanchez in their colours when this mood grabs him.
Key Opta stats:
- Arsenal have now won their last 11 games at the Emirates in all competitions, their second longest ever run at the ground (12 between May-November 2009).
- Brighton have never won an away match against Arsenal in all competitions, drawing once, losing six times and scoring just one goal.
- Arsene Wenger has now beaten 45 different clubs in the Premier League, more than any other manager in the competition.
- Alexis Sanchez has had a hand in 35 Premier League goals since the start of last season (24 goals, 11 assists), more than double any other Arsenal player in that time (Mesut Ozil, 17).
- Nacho Monreal scored his fourth goal for Arsenal in all competitions, with each coming at a different ground (Liberty Stadium, Old Trafford, Wembley and Emirates).
- The Gunners have kept four successive Premier League clean sheets for the first time since May 2014.
- Alexis Sanchez created twice as many chances (6) and had twice as many shots (8) than any other Arsenal player.
- Brighton have scored just one goal in their four Premier League away games so far this season.