Aberdeen boss Steve Paterson was forced to make three changes to the side that drew 1-1 with Livingston on Saturday with central defensive partnership of Russell Anderson and Alexander Diamond along with midfielder Steve Tosh all failing to shake off knocks.
Also missing from Saturday's line-up were Richard Foster and Bryan Prunty who were dropped to the bench.
The Partick Thistle management team were also forced to make changes with Milne and Fleming suspended. This meant a first start for former Celtic forward Jorge Paulo Cadete since his recent move to the club.
Thistle also made three further changes to the side that went down 3-0 to Dunfermline at the weekend.
The home side made a bright start to the match and in four minutes a Chris Clark cross presented David Zdrilic with a chance but he could only head into the arms of Langfield.
Thistle's first effort at goal was a Billy Gibson header just the wrong side of the upright.
On 17 minutes only a last ditch goal-line clearance from Grant Murray prevented the home side taking the lead from Clark's crisp shot from the corner of the six yard area.
On 34 minutes, the Dons were gifted the chance to take the lead when referee John Rowbottom awarded them a spot kick after Leigh Hinds was up-ended inside the area.
Paul Sheerin stepped up to take it sending it to keeper James Langfield's left but he was up to the task and parried the ball away and the chance had gone.
13 minutes into the second half Aberdeen's Zdrillic had another good chance from eight yards but his right foot shot was again brilliantly saved by Langfield.
On 65 minutes, Langfield was again called into action blocking another effort by Aussie striker Zdrillic.
The onslaught continued and on 72 minutes some fine work by Hinds ended with a low cross along the six yard area. It looked like nothing more than a simple tap in for Phil McGuire but he somehow managed to steer it beyond the foot of the post.
With three minutes remaining Aberdeen boss Steve Paterson gave a top team debut to young striker John Stewart when he replaced Zdrillic.
At the end of the game, Paterson must have been left wondering how his side failed to take all three points in a hugely one-sided affair.
As for Partick Thistle, they now seemed destined for first division football next season and on the evidence of tonight's performance they will not have too much to complain about.