The decisive boot -- Brown's third field goal of the game -- helped New York overcome an anemic offense that produced just 57 total yards in the second half.
The Giants (6-9) converted 17 points off three Detroit turnovers, capped by a score-tying, 38-yard interception return for a touchdown by Will Hill with 4:57 left in regulation.
Eli Manning made good on 23-of-42 passes for 256 yards with an interception and a touchdown to Jerrel Jernigan, who finished with six grabs for 80 yards.
Detroit (7-8) dropped out of the playoff picture after blowing a late lead for fifth time in six contests -- all of them losses.
Matthew Stafford completed 25-of-42 passes for 222 yards with a pair of interceptions.
Joique Bell supplied 154 yards of offense with a 1-yard TD run for the Lions.