BSOD playing Borderlands 2, error 0x000000e1 (?)

Stress test the Graphics Card using Furmark.
Video Card - Stress Test with Furmark

It is to be sure that the card is not causing the problems.

Alright I have done this test, there didn't seem to be any problems....
MAX TEMP: Leveled out at 75 C

I saw no artifacts and the pc seemed to be running smoothly

Good news that the card is OK.

Reduce the priority settings of those games. It may make the situation a bit better.

It is caused by avast! TDI Filter Driver.

Code:

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Use !analyze -v to get detailed debugging information.

BugCheck 3B, {c0000005, fffff88002c7b039, fffff880153ada80, 0}

Probably caused by : aswTdi.SYS ( aswTdi+5039 )

Followup: MachineOwner
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Uninstall Avast using Avast Uninstall Utility.
Use Microsoft Security Essentials as your antivirus with windows inbuilt firewall, and free MBAM as the on demand scanner.

Download and install those, and then run full system scans with both of them, one by one.

Let us know the results.