I've had issues with a 2002 ES300 when the vacuum lines were hooked up properly, the car would stall. It was a combination of a disconnected vacuum switching near the motor mount and another broken vacuum switching valve underneath the engine cover. I also cleaned out the throttle body and reconnected everything properly and ran new vacuum lines. Left the battery unplugged to clear out the ECU and replug it back in. Everything worked perfect afterwards.
If your car is stalling right after starting, might have to hold the gas down and keep it running until the ECU can re-learn the changes in the air intake. If the car is not running right with the intake in with the proper connection, something else is going on.
For what it is worth, I am using an Injen Intake in my 2004.
There is a piece of a filter paper on the open port as seen in the picture. I been trying to find a plastic cap as there was suppose to be another vacuum hose for the 3.3L IIRC. The instructions for the Injen to cap it off if it wasn't the 3.3L IIRC but my 'used' kit didn't have a cap nor was it included with the kit per instructions. It is a vacuum leak since it's past the MAF