The primary mechanism of power used by unions to keep wages high is by reducing the available work force. This is done by lobbying for things like requiring certifications to be legally allowed to perform work and lobbying/negotiating for disallowing non-union members from accepting work. This has the net effect of increasing the wages of the high paid workers while reducing the wages of the low paid workers who could do the higher paid work but aren't allowed to.

Here's Nobel economist Milton Friedman discussing it in more detail. https://www.youtube.com/watch?v=xzYgiOC9cj4