1991 cutlass supreme 3.1 engine, replaced fuel pump , engine runs a few minutes, than shut off, what is the problem?

is the fuel filter part of the fuel pump or is it separate? if it is separate, have you changed the fuel filter?

I have a 3100 also. It's a 96. Filter is NOT in the tank. It should be changed. In tank strainer should have been changed with the pump. Also if the pump died, you should have checked the connector plug. If may have been damaged by the old pump. It could be any number of things. What's the fuel pressure? Did you check that before you changed the pump? Crankshaft sensor should be under the block near the firewall. I'd check the pressure first. If it's going wonky troubleshoot the pressure regulator. You'll need a vacuum pump. You should always check the plugs too. Been reading up on my car as I'm having a fuel issue. Can't tell you how many people have changed the fuel pump before they bothered to check the plugs. You need to diagnose the cause of the problem before you change any more parts.

One more thing! I've read the VIN-M has 2 sensors. One in the front and the one in the back. Don't know if that's true in your case as it's a 91.

pressure regulator

Check crank sensor 3x or 7x for 2v ac voltage, and as the car is cranking, the voltage should vary. Do ohms test too. The sensor should between 500 and 900 ohms. If the sensor is bad, check the wiring harness by doing an ohm check. If the sensor is bad, you are in for a tough job. Easiest way to get the sensor out, is to remove the coli pack assembly, reach down and put 3/8 ratchet with a 10 mm socket on it, and loosen the bolt. Then raise the car up, get a pry bar, and gently tap on the pry bar, as you slowly rotate the sensor around, it will pop out. If you use brute force, you will break it off, then it's a real pain to get it out.

I've solved this problem by replacing the injectors. Guaranteed fix. I went to the auto wreckers and picked up the fuel rails and injectors for $90.00 dollars. Runs like a brand new car.