How wide is the driveway? And how much room do you have on either side of it? I've "burrowed" under driveways using water and pipe, but you need to get below the stone under the driveway bed so you need room on at least one side to lay about a 10 ft pipe on the ground and get a water hose attached to it. To stay level under the driveway you need a trench deep enough to get the pipe laying pretty level at an elevation that's below the stone base below the pavement. If you have good water pressure you can actually push the pipe under the driveway.

My longest run doing this is only about 20 ft so if it's a REALLY wide paved area, this probably won't work.

It's messy, to be sure, but if you have the room and some time, it beats having to saw-cut the pavement, trench across, and then patch it.

Sidewalks are a BREEZE using this method. Also depends on soil conditions, obviously, but it's a valid approach and works quite often.