Rahm and Stenson led after two rounds and stay locked together after both posted third-round totals of 69 at New Providence in the Bahamas.
They have been joined by Finau, who followed up a 64 with a 67. The 29-year-old bogeyed the second hole but did not drop another shot while posting six birdies.
England's Justin Rose is out of the picture (Getty)
Gary Woodland managed the same score to sit in fourth place, two shots behind. Rickie Fowler also hit a 67 and is another shot further back.
Host Tiger Woods had a less enjoyable afternoon, dropping three shots in the first three holes in a 72 that leaves him bottom of the leaderboard. Woods at least repaired some of the damage and finished with birdies at 15 and 17.