Lindell missed an attempt at the end of regulation play but had made two earlier, from 33 and 25 yards.
Jones ended up with 208 yards rushing on 21 carries.
Fitzpatrick replaced starter Trent Edwards, who suffered a head injury, in the second quarter and ended up with 10 completions for 116 yards.
The Bills are 2-4 and the Jets 3-3.
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