Having another offer in hand gives you leverage. It signals to your current employer that the market is willing to pay more than your employer pays now. I would not dismiss using it to get more compensation. Just don't present it as a threat. Just be straight forward to your manager. Tell him/her that the offer makes it very hard for you to justify to stay and if they can do something about the compensation to make it worth your while.

An employer that doesn't understand that an employee would leave over a significantly better offer is an employer that you don't want to work for to begin with.