not in a single season...just most consecutive wins in a row...
From:
http://www.profootballhof.com/history/release.jsp?release_id=130621 Games
New England
Patriots
2003-2004
Win Date Opponent, Score
1 Oct. 5 Tennessee Titans, 38-30
2 Oct. 12 New York Giants, 17-6
3 Oct. 19 at Miami Dolphins, 19-13 (OT)
4 Oct. 26 Cleveland Browns, 9-3
5 Nov. 3 at Denver Broncos, 30-26
6 Nov. 16 Dallas Cowboys, 12-0
7 Nov. 23 at Houston Texans, 23-20 (OT)
8 Nov. 30 at Indianapolis Colts, 38-34
9 Dec. 7 Miami Dolphins, 12-0
10 Dec. 14 Jacksonville Jaguars, 27-13
11 Dec. 20 at New York Jets, 21-16
12 Dec. 27 Buffalo Bills, 31-0
13 Jan. 10 * Tennessee Titans, 17-14
14 Jan. 18 * Indianapolis Colts, 24-14
15 Feb. 1 ** Carolina Panthers, 32-29
16 Sept. 9 Indianapolis Colts, 27-24
17 Sept. 19 at Arizona Cardinals, 23-12
18 Oct. 3 at Buffalo, 31-17
19 Oct. 10 Miami Dolphins, 24-10
20 Oct. 17 Seattle Seahawks, 30-20
21 Oct. 24 New York Jets, 13-7
Streak Ended Oct. 31 at Pittsburgh Steelers, 20-34