Enjoying company from family makes Wu feel good which has impacted his game.
Johnson built a 16-under par total of 197 at Club de Golf Chapultepec, where McIlroy fired a three-under 68 for 201.
Johnson's methodical approach at Club de Golf Chapultepec paid dividends as he overhauled first-round leader McIlroy.
Wade Ormsby settled for a tie for second with fellow Australian Brad Kennedy.
The pioneering tournament is the only one in the world with male and female fields, playing in alternate groups on the same course and for equal prize money.
It was the first time since the European Tour started keeping records in 1999 that a player made three birdies on a par-4 hole.
Garcia thus became the first player on the European Tour to be disqualified under Rule 1.2a, which deals with player conduct.
For the American veteran, playing on a sponsors invite, it was his best round on the European Tour since the final round of the 2009 Hong Kong Open.
It was Woods' worst weekend on Firestone's South Course since a 75-77 finish in 2010.
The trio made the most of perfect morning scoring conditions, finishing the second round on 11-under 129.
Poulter had eight birdies without a bogey to hold a one-stroke lead over Americans Kyle Stanley and Rickie Fowler.
World number 23 DeChambeau looked in danger of slipping off the top of the leaderboard after a slow start, but a run of four birdies in his final seven holes saw him sign for a four-under-par 68 and a 10-under total.
World number 322 Dantorp, who has not even managed a top-10 finish this season, poured in a birdie putt on the 18th late in the day to sign for a two-under-par 68 and reach 13-under par for the tournament.
The 44-year-old Dredge, who won the last of his two European Tour titles back in 2006 at the European Masters, carded a four-under par 67 on a day when only 14 players broke par for the first round.
The 28-year-old Dane, one stroke behind Slattery after the third round, finished on a 22-under 262 for his first title since the Turkish Open in November 2016.
Slattery had led during the second round only to drop three shots in two holes on Friday.