With their four goals coming in the final half hour, United did not have it all their own way.
Even though the home side lost Gabriel Reuben early in the game for two yellow cards inside the space of five minutes it took the visitors some time to assert their authority.
Mackay-Steven said: "We weren't at our best, especially in the first half, but after they had a player sent off we were told just to be patient.
"In the end we scored four goals. Kilmarnock played well in patches and will feel a bit hard done by, but it was difficult for them down to 10 men.
"It was great to score as many goals for the fans, who travelled through in terrible weather, for the players and particularly for Stuart Armstrong, who was superb."
It was Armstrong's influence in the second half which put United firmly in control.
His run and delivery from the goal-line allowed Keith Watson to blast United ahead just short of the hour mark.
Then two goals inside two minutes, the first a great solo effort from Armstrong and the neat a tap-in from Ryan Gauld after Armstong's effort was palmed out by Craig Samson, put them in command.
United boss Jackie McNamara was delighted with another good win, irrespective of the recurring score line.
He said: " The players haven't spoken about scoring four goals in games recently, they are just interested in keeping going to the final whistle.
"We are always confident of scoring, whether in the first minute or the last and even when the subs come on they are keen to get involved and grab a goal."
That was reinforced when striker David Goodwillie, on loan and more often on the bench, came on to grab the fourth goal in injury time.
The dismissal of Reuben after only 22 minutes influenced the game and Allan Johnston thought that both the ordering off and the effect it had were unfair.
Reflecting on his team's efforts the Kilmarnock boss said: "It was always going to be a hard game against a team with United's confidence but I didn't think there was much in the game before the sending off.
"The first booking was harsh and I think perhaps the referee was too keen to get his cards out. I can't complain about Gabriel's second booking but going down to 10 men is frustrating and spoils the game for everyone."
Johnston was especially pleased with the performance of 19-year-old Craig Slater.
"One of the big positives for me was young Craig. I thought he was fantastic. We were down to 10 men and he was running the game for us."
The Rugby Park boss also had a word of praise for Kris Boyd who grabbed his side's consolation goal two minutes from time.
However, in a game where the goal statistics were notable, Boyd's strike took his total with Kilmarnock and Rangers to 175, taking him past Henrik Larsson's record for the Scottish top flight.
But following the home defeat Boyd was modest as he reflected on his haul.
"At the end of the day it's the team that matters and it was another disappointing result.
"On a personal note fine, although I would like to have scored a winning goal, and when you finish your career you can look back on the record but at the moment it its about the team's performance."