Lee has made a solid start to the 2013 season. He has made three out of four cuts and his best result came when he finished tied sixth at the Chile Classic in March. He also finished in a share of 13th place at the season opening Sony Open in Hawaii on the PGA Tour.
The former European Tour winner is back on the Web.com Tour after failing to keep his card on the PGA Tour in 2012.
He missed out in qualifying school by one only one shot.
Lee, who is currently 26th on the Web.com Tour money list, needs to finish inside the top 25 players to return to the PGA Tour in 2014.
Fellow Kiwi Tim Wilkinson is also in the hunt this week in Brazil. The left-hander from the Manawatu carded a two-under par 69 in round three to be alone in ninth place.
The former PGA Tour professional, who is 16th on the Web.com Tour money list, is on a 10-under par total and seven shots back from the leader Alvarado.
Hamilton professional Steve Alker dropped 24 places to a share of 42nd after a one-over par 72 in round three to slip back to a four-under par total.
But the main interest is on Lee to see if he can shoot a low score tomorrow and claim his first title in almost two years.