The Suwon Bluewings striker repaid Arnold’s faith with a first-half double – just as he did the last time Australia played Taiwan back in 2012.
Taggart opened the scoring after 12 minutes with a diving header from a Rhyan Grant cross for his first international goal in six years.
Two more of those given a start – Awer Mabil and Brad Smith – then combined well on the left with a slick one-two before Taggart tapped home a Smith cross in the 19th-minute.
Rather than roll over, Taiwan showed their skill with a fine goal two minutes later when Chen Yi-Wei ghosted between central defenders Milos Degenek and Souttar to send a bullet header past Mat Ryan.
It was the first goal conceded in the qualifying campaign by the Australian goalkeeper who was captaining his nation for the first time in his 58th appearance.
Australia restored their two-goal advantage in the 33rd minute when a great crossfield ball by Aaron Mooy found Grant in space and his right-wing centre was smashed home by Irvine.
The Hull City midfielder added his second three minutes later when he headed home a teasing Mabil cross in the 36th minute, ensuring Australia went in at halftime with a healthy 4-1 lead.
Irvine had a chance to claim a hat-trick after the restart following more good work by Smith and Mabil, but blazed over the bar from inside the box.
Arnold’s decision to replace the ineffective Brandon Borello with Ajdin Hrustic proved the source of a late flurry by the Socceroos.
Hrustic twice found the head of Souttar – who now has three goals from his first two Socceroos appearances – and he also set up Maclaren’s second-half strike as Australia delivered the ruthless edge Arnold has been demanding all campaign.