The Nevada tournament is run under modified stableford scoring and Wilkinson's round today (fri) included nine birdies and two bogeys, which gave him 16 points and he is in second alongside Australian Geoff Ogilvy.
American Nick Watney, who made nine birdies and as many pars during the first round, is in the lead on 18 stableford points.
The Barracuda Championship, which changed its scoring to modified stableford in 2012, is the only tournament on the PGA Tour, which uses this format.
Players are awarded points on each hole with eight points for a double eagle, five for an eagle and two for a birdie. Scoring par on a hole is neutral while a bogey costs you one point and a double bogey or worse will result in a player losing three points.
Essentially, the format promotes 'risk and reward' on the golf course and encourages players to take on more aggressive strokes in the search for points, while if they're on track for a double bogey or worse they can just pick up their ball and move on to the next hole.
This week's tournament has a watered-down field given the world's best players are on course at the World Golf Championships-Bridgestone Invitational event in Akron, Ohio.
Wilkinson began the week in 108th on the FedEx Cup points standings and while a consistent end to the season would see him finish inside the top 125 players and retain his tour card, he could create some comfortable breathing space with a big week at the Montreux Golf and Country Club.
Fellow Kiwi Danny Lee also enjoyed a solid opening day in Reno as he picked up 11 stableford points with a round that included six birdies and a bogey that left him in a share of 10th.
Hamilton's Steven Alker has taken a week off on the second-tier Web.com Tour and skipped the Stonebrae Classic in California.
Meanwhile, there is no LPGA Tour event scheduled this week meaning Lydia Ko will likely return to action next week at the Meijer LPGA Classic in Michigan.
