Leeds struck back just before the break through Michael Bridges but City won comfortably to record their first back-to-back wins of the season.
Lee Croft should have opened the scoring within 2 minutes after rounding the Leeds keeper but shot wide with the goal at his mercy. However, the England U19 midfielder made no mistake after beating the offside trap 5 minutes later.
Macken then played Elliott in to score the second on 27 minutes, just as he had done against Blackburn last week. Elliott then returned the favour on 37 minutes before Macken's shot squeezed under Shaun Allaway.
Leeds featured Didier Domi, Michael Duberry and Nick Barmby but it was City's senior pros, Richard Dunne and Gerard Wiekens, who impressed as City held firm to secure the points.
Simon Johnson managed a couple of attempts at goal for Leeds but they were well dealt with by City keeper, Kasper Schmeichel.
City: Schmeichel, Flood, Jordan, McCarthy (N D’Laryea 62), Dunne, Bischoff, Croft, Negouai (J D’Laryea 72), Macken, Wiekens, Elliott.
Subs: Ellegaard, Onouha, B Wright-Phillips.
Leeds: Allaway, McStay (Armstrong 46), Domi, Woods, Duberry, Richardson, Lennon, Bridges (Stiens 76), Chapuis (Winter 46), Barmby, Simon Johnson.
Subs: Krief, McDaid.
Attendance: 1,058.