Substitute Mohamed Chalali's headed goal with his first touch was down to good fortune and not managerial genius, admitted Aberdeen manager Craig Brown.
Trailing to a Jon Daly strike, Brown sent on Chalali with 25 minutes remaining at Tannadice and he soon headed home a Rory McArdle flick-on.
"When your sub scores with his first touch, that's lucky," said the manager.
"But the substitutions in general worked for us. That was probably the key to our victory."
And Brown, who had sent on goal provider McArdle five minutes before Chalali, then Chris Clark for Rob Milsom in 82 minutes, added: "We made the appropriate changes in shape and personnel.
"Sometimes the substitutions work for you, sometimes against you."
Aberdeen's win was secured in spectacular style. With four minutes left, Kari Arnason hammered the ball in off the underside of Dusan Pernis's crossbar from 40 yards.
Brown was angry at his team's first-half display and told BBC Scotland that his players were on the receiving end of "harsh words at half-time".
"We were not at all impressed with the first 20-25 minutes in particular. They were told that in no uncertain terms," he said.
"It was a tense game. It was end to end and we were fortunate to win. I think Dundee United will feel unfortunate to lose the game.
"But we showed tremendous endeavour and character to win that game from 1-0 down."
The Dons took a travelling support of more than 4,000 fans to Tayside and Brown insisted that the victory was a thank-you to them.
He said: "I've got to credit the 4,071 fans that came from Aberdeen. That's a home gate for quite a number of SPL clubs; that was an away support for us.
"The support we had when we were a goal down was tremendous.
"I still marvel at the Aberdeen support and I want to thank them for coming."
"On play, a fair result would have been a draw. But we've had so many games this season when I have said we deserved more than we got.
"Probably we got more than we deserved but the fans deserved it and I am delighted for them.