All ICs in the libraries have the power pins available for the schematic. Some of them are hidden by default but you can get them using INVOKE. Once you have them on the schematic you can explicitly connect them to whatever power net you want. Granted this does tend to create ERC warnings but you can ignore (or approve) them.
An alternative approach, though it's more effort, would be to create your own libraries where all the ICs follow the same convention. This would avoid Eagle issues but your libraries would then not match the IC manufacturer's data sheets.
It's also possible to connect nets using a link or "star point" device (two schematic pins with overlapping pads on the board) but your question suggests you aren't doing something that wants that approach.
