Taggart has set the K League 1 alight this season and continued the trend in a 3-1 win over fourth-placed Gangwon FC on Saturday night.
The 26-year-old's treble took his league-leading tally to 16 for the season - six clear of Ulsan Hyundai's Kim Bo-kyung and Junior Negao - and now leaves Suwon in sixth place ahead of Sangju Sangmu's clash with Pohang Steelers on Sunday night.
Mooy meanwhile took the field for Brighton on Sunday morning, coming on in the 85th minute to secure the Seagulls a 1-1 draw with West Ham United.
The 28-year-old replaced goalscorer Leandro Trossard, who equalised just four minutes after Javier Hernandez put the Hammers in front on the hour.
Goalkeeper Mat Ryan was again strong between the sticks, making two saves to maintain his side's unbeaten start to the Premier League season.
Fellow Socceroo Borrello also made his debut overnight, playing 65 minutes in Freiburg's 3-0 victory over Mainz.
The former Brisbane Roar forward was named in the starting line-up by manager Christian Streich, before being replaced by eventual goalscorer Lucas Holer.
Holer's effort opened the floodgates for the home side, who soon went further ahead through Jonathan Schmid and Luca Waldschmidt.
Borrello's Bundesliga debut comes after a raft of injuries stuttered his development in Germany with third-tier side FC Kaiserslautern.
In the Championship, Jackson Irvine played the full 90 minutes as Hull City settled for a 1-1 draw away to Brentford.
Jarrod Bowen's 53rd-minute strike put the Tigers in front, only for Bees forward Ollie Watkins to equalise less than 20 minutes out from full-time.
Victory also eluded Massimo Luongo, whose 59th-minute introduction failed to lift Sheffield Wednesday from a 1-0 defeat to Millwall.
The Lions took the lead through Matt Smith in the 37th minute and held on despite a red card to Jed Wallace just six minutes later.
Socceroos captain Mark Milligan was also without a win this past weekend as Southend United fell 4-0 away to League One leaders Lincoln City.
Milligan was named in midfield by manager Kevin Bond but failed to stifle a City side unbeaten through three matches.
And in Serbia, Milos Degenek was an unused substitute as Red Star Belgrade continued their winning start to the Serbian SuperLiga with a late 3-2 victory over Spartak Subotica.