Down led by 1-5 to 0-6 at half-time thanks to a goal from Liam Doyle as Down started in a frenzied fashion.
Jim McGuinness’ side kept their composure however and hit back thanks to a brace of points from Mark McHugh before the interval.
There was little between them in the third quarter before Donegal hit the front for the first time when Martin McElhinney blasted home.
But Down responded with four points and while Molloy reduced the deficit in the closing minutes, he was unable to grab a deserved equaliser.
The men form Tor Conaill may not have changed their style and kept plenty of players behind the ball but they broke with pace and used the open spaces well.
However, their plan was countered by experienced Down centre-back Liam Doyle who broke forward at every opportunity and he fired home a goal which opened up a 1-03 to 0-01 lead after just seven minutes after Down had landed three points inside three minutes of the start.
Donegal responded with Mark McHugh kicking a brace of points and Patrick McBreaty pointing a free as Down fought back to leave it 1-05 to 0-06 at the interval.
The sides exchanged points after the restart and after Anthony Thompson had reduced the deficit to a point, Donegal hit the front.
Martin Reilly and Neil Gallagher combined to send Martin McElhinney through for a goal which pushed Dongeal into the lead for the first time after 51 minutes.
But they managed just one point after that as Down responded with four points in a row with Doyle getting two more frees and Conor Garvey and Brannigan also finding the range.
Molloy reduced the deficit with a point from play but then missed the chance to grab a draw in an exciting finish.
Down scorers: L Doyle (1-04, 0-02 frees); A Brannigan (0-02); B Coulter (0-01); C Garvey (0-01); A Carr (0-01, free); D Gordon (0-01).
Donegal scorers: M McElhinney (1-00); M McHugh (0-02); P McBrearty (0-02, both frees); S Griffin (0-02, both frees); D Molloy (0-01), K Lacey (0-01), A Thompson (0-01).
Down: B McVeigh; O Costello, D McCartan, K Quinn; A Brannigan, L Doyle, D Turley; P Turley, D Gordon; G McCartan, A Carr, M Poland; M Miskelly, C Laverty, B Coulter.
Subs: R Brady for Miskelly, 32; C Garvey for Coulter, 49; N McParland for Quinn, 52; A Rogers for Brannigan, 52; E McCartan for Poland, 68.
Donegal: P Durkan; F McGlynn, N McGee, P McGrath; A Thompson, K Lacey, L MacLoone; R Kavanagh, N Gallagher; D Walsh, M McHugh, C Classon; R Bradley, P McBrearty, S Griffin.
Subs: M McElhinney for Classon, 25; M Reilly for Walsh, 35; D Molloy for Griffin, 49; A Hanlon for MacLoone, 67.