How to control a momentary switch from the web via a smartphone?

So we have an electronic gate that uses a push button momentary switch for opening and closing. The button itself is not unlike a doorbell or garage door button. I've been trying to figure out a way to remotely control this button from the web via a smartphone.

I've looked around and found all number of light switches and power outlets that can be web controlled, but can't seem to locate a momentary relay for my purposes. I was hoping to be able to patch into or replace the existing button with something that would give me the capability, but without breaking the bank. 

Is there a momentary relay out there that can easily be connected to my home network? 

Thanks.

Any relay or transistor can replace that button. All relays are momentary. They only switch as long as you apply current to there coil. So if the button only needs to be activated for a second then only energize the coil for the relay for a second. If the current through the button is low then a transistor can be use. Just apply power to the base of the transistor for as long as the button needs to be pressed.

If you like Arduino then take the arduino of your choice, an Ethernet shield and a transistor and make that system work. Replay the button with the transistor and your ready to role. The arduino will apply 5V to the transistor's base which will allow current to flow from the collector to the emitter thus closing the circuit.