Senior has played in 94 tournaments without a win, but in the process has collected $4.2 million.
His 8-under 63 Thursday at the TPC-Harding Park course put him one shot in front after the opening round of the tour's final event of the season.
The yearlong points race will be concluded this week and Kenny Perry heads into the tournament in excellent position to win the Charles Schwab Cup.
Perry leads the points race and the only other player with a chance to finish in front of him is Bernhard Langer.
To win the Charles Schwab Cup, Langer must win this tournament while Perry is finishing outside the top five.
Langer opened with a 67 Thursday to tie for fifth place with Steve Elkington and Duffy Waldorf. Perry was in a six-way tie for eighth after firing a 68.
Senior made nine birdies in his opening round and also eagled the par-5 ninth.
Swim Week Miami Beach 2014 [PHOTOS]