Arsenal, who have also claimed back-to-back Europa League wins and a Carabao Cup triumph since losing at Anfield, now head into the worldwide break level on 13 points with fourth-placed Chelsea and six behind the table-topping Manchester clubs.
Brighton also hit the post, when a set piece gave Marsh the opportunity to strike from range.
Forced to attack, Brighton was far better from then on and could even have gone in level at half time.
Arsenal doubled their lead after the break. Sead Kolasinac had some problems, but he is available.
Sanchez turned in a virtuoso performance after half-time, with his standout moment of brilliance making the points safe in the 56th minute.
As Olivier Giroud stood on the touchline ready to be substituted into the action, Sanchez played one more wall pass with Lacazette before the latter was withdrawn.More news: 50 arrested in MA amid federal immigration sweep
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"They defended with a lot of players".
However, the Gunners did take the lead in the 16th minute when Monreal found the net from around 12 yards out after Brighton had earlier cleared off the line during a scramble inside the box. Ramsey popped the ball back into the path of Sanchez, who held off a swarm of Brighton defenders before digging out a superb back-heel to free Iwobi.
Play your top scorer from last season alongside your club record summer signing and you're left with an exciting, effective partnership, right?
- Arsene Wenger has now beaten 45 different clubs in the Premier League, more than any other manager in the competition.
Arsenal were in control of the game and a neat one - two between Alexis Sanchez and Alex Iwobi saw Iwobi's low effort saved by Matthew Ryan in the Brighton goal.
- The Gunners have kept four successive Premier League clean sheets for the first time since May 2014.
Sundays are the new Saturdays for Arsene Wenger's men, who produced their most impressive display of the season a fortnight ago against Chelsea, before backing it up with three wins concluding in a 4-2 triumph at BATE Borisov on Thursday night.