Delbonis is one of the only players in the world to have a 100 per cent record against the Swiss star going into the competition.
The world No 67 beat Federer on clay in Hamburg in 2013, but the Swiss star is out for sweet revenge in California.
However, he will now have to wait until this afternoon for play to resume after rain fell overnight on the west coast of the United States.
Federer will take to court after Novak Djokovic.
Rain delayed the start of the match as both players sat court-side under umbrellas while the ball boys and girls padded the ground with towels.
However, when play got underway Federer continued his fine form which saw him win the Australian Open and Rotterdam Open.
The 36-year-old won the toss and opted to serve first and he was almost forced to regret that decision when Delbonis took him to deuce.
But Federer held his serve before breaking for a 3-1 lead in the fourth game.
Both players continued to see out their service games as the world No 1 took the first set 6-3.
The match was closely-fought in the second set as the pair held their serve in the first four games.
But with the score tied at 2-2 rain began to lash down on the turf and the players were pulled off by the umpire.
The crowd quickly dispersed and headed for cover before the game was abandoned.