United recovered from last weekend's 2-0 defeat to Scottish Cup final opponents St Johnstone to cut the gap on Motherwell to four points and maintain their hopes of a top-three finish.
Donnelly, supervising matters from the dug-out as Jackie McNamara served a touchline ban, said: "That's the most pleasing thing for us as coaches, we look for a response. We were really disappointed last week and I think the boys felt it as well.
"The gaffer had a collective meeting with them on Monday and we have worked really hard this week, and it has culminated in a great response today.
"We were all hurting after last week, it wasn't acceptable, but the response was brilliant."
Motherwell manager Stuart McCall, who saw his side slip four ponts behind Aberdeen in the race for second, said: "I will sum it up as briefly as I can - they were very, very good and we were very, very poor.
"They have had the measure of us this season and their strengths have been on the counter-attack.
"If you look at the first three goals, one was from a corner from us and the other two, we had the ball on the edge of their 18-yard box, and they break with such pace and desire. We were second best in every department."