Duffy passes out of defence, both of which resulted in John McGinn shots from the edge of the area with the second coming immediately before the Republic's second goal.
But this was clearly the Republic's day and Obafemi put the game beyond Scotland when he lashed a fierce right-footed shot past Gordon after Billy Gilmour had lost the ball in a dangerous position.
Aside from Hogan being denied by Hanley, the Republic dropped off after Obafemi was withdrawn in the 56th-minute because of injury but the home side's third goal had effectively killed the game as a contest with Scotland failing to muster a meaningful response.
Clarke's side must now look to do that by managing what the Republic could not by beating Armenia in Yerevan on Tuesday (17:00 BST) while the Irish will hope to maintain momentum when they travel to Poland to take on Ukraine later that evening (19:45).
Scotland's first defeat in Ireland since 1963 - match stats
Republic of Ireland have won their first ever game in the Nations League at the 13th attempt of trying (W1 D5 L7), scoring more goals (3) than they managed in their first 12 matches in the competition combined (2).
Scotland suffered just their second away defeat to Republic of Ireland (P7 W2 D3 L2) and first since June 1963 (1-0).
This was Republic of Ireland's biggest competitive win on home soil since October 2014, when they beat Gibraltar 7-0 in a European Championship qualifier.
Republic of Ireland had two players aged 21 or under (Michael Obafemi & Troy Parrott) score in a competitive game for the first time since September 1997 (David Connolly & Mark Kennedy vs Iceland).
Parrott (20y 127d) became the youngest player to score a competitive goal for Republic of Ireland since Stephen Ireland in October 2006 (20y 46d vs Cyprus in a European Championship qualifier).
Obafemi and Parrott became the first players to both score and assist in a competitive game for Republic of Ireland since both Robbie Keane and Wes Hoolahan did so against Gibraltar in October 2014.
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