Arsenal kept coming close at the other end and Lewis Dunk had to clear off the line after another corner in the 68th, while Martin Odegaard drew the only quality save from Verbruggen when he drove into the area and unleashed a fierce shot that needed a one-handed stop.
Havertz headed high from six yards out after the ensuing corner, while Brighton came closest to an equalizer in the 83rd when Pascal Gross met a cross from Kaoru Mitoma but sent his shot just wide of the near post.
Just as it looked like Arsenal might be made to pay for all those misses, substitute Eddie Nketiah released Havertz on a counter and the Germany forward beat Verbruggen with a left-foot shot inside the far post.
The win lifted Arsenal two points ahead of Liverpool ahead of their match against Manchester United. It also put the Gunners five points ahead of Manchester City after the defending champion was held to a 2-2 draw by Crystal Palace on Sunday. Aston Villa is one point behind Arsenal.
EPL results: West Ham ease by Wolves
What a difference a week makes in the Premier League. Seven days ago West Ham suffered a 5-0 thrashing by Fulham but this morning turned things around with a 3-0 win over Wolves.
Mohammed Kudus scored twice in the first half and Jarrod Bowen added a third in the 74th minute to put West Ham into seventh.
EPL results: Liverpool 0 Manchester Utd 0
Liverpool were left frustrated after failing to secure a home win over their old rivals. It’s the first time since January that Liverpool failed to score at home as they missed the chance to move back to the top of the table. The draw leaves them a point behind Arsenal before the two sides square off on Christmas Eve (NZT).
EPL ladder
(Team, points)
1. Arsenal 39
2. Liverpool 38
3. Aston Villa 38
4. Man City 34
5. Tottenham 33
6. Newcastle 29
7. Man United 28
8. West Ham 27
9. Brighton 26
10. Chelsea 22
11. Fulham 21
12. Brentford 19
13. Wolves 19
14. Bournemouth 19
15. Crystal Palace 17
16. Everton 16
17. Nottingham Forest 14
18. Luton Town 9
19. Sheffield United 8
20. Burnley 8