The first line of defense is plumbers putty under the lip on the top side of the sink. I also see the the sink was not cut flat. Put some plumbers putty between the gasket and the sink.

The leak is not coming from the gasket. In the first picture the leak is starting from where the threading begins on the pipe (See the green looking stuff). Everything above that thread is dry, the leak is starting where the threading is and trickling down. I suspect I would have to unscrew the bottom pipe, wrap teflon tape and screw it back together but I want to avoid that if I can. I was wondering if I could put some paste where the threads connect to the bottom part with the gasket instead of taking apart the plumbing at the bottom and creating more mess.