"The Power" struggled on the doubles in the early part of the match, and despite hitting sparkling finishes of 93 and 105 under pressure, had to rely on Green missing double-18 and double-nine before edging to a deciding leg victory.
Target's five-time World Champion Raymond van Barneveld also kept up his 100% record, but had to fight back from three legs down to Welsh number one Gerwyn Price - defying an average of 101 from his opponent to win 5-4.
However, Target teammate Rob Cross suffered an agonising defeat to world number one Michael van Gerwen, as he averaged in excess of 104 but missed two darts at double-top for a 5-3 victory, before succumbing in a last leg decider.
Ex-Lakeside Champion Stephen Bunting is top of his group after prevailing in the all-Target encounter with former Runner-up Dave Chisnall 5-2, while Alan Norris fell to a 5-3 defeat to Glen Durrant, and Joe Murnan is yet to register a point following his 5-3 loss to Ross Montgomery.
Bunting knows that victory over Scott Mitchell on Monday night will see him qualify on top of Group F, while "Chizzy" must beat Jeffrey de Zwaan to give himself the best chance of progressing through the same group.
Norris, meanwhile, has a straight shoot-out for a place in the last 16 with UK Open Champion Peter Wright.
The remaining members of #TeamTarget: Taylor, van Barneveld, Cross and Murnan all have a day off, before returning to action on Tuesday evening for their final group stage ties.
You can follow their progress live on Sky Sports in the UK, and worldwide via the PDC's broadcast partners.