Hearts manager Craig Levein praised his team's determination to atone for an "embarrassing" display after they knocked Motherwell out of the Betfred Cup.
Sean Clare missed a penalty for Hearts before goals late in the first half from Michael Smith and Conor Washington put them in command at Fir Park.
The visitors held on for a 2-1 victory without major scare after Christopher Long pulled a goal back on the hour mark.
Levein was delighted to put the previous weekend's goalless draw with Ross County behind them as well as reach the last eight.
"Last week I just can't explain, I don't know what happened, but it did give us an opportunity to talk about what's expected when you play for Hearts and the performance that is required," he said.
"I know the players were slightly embarrassed, and so was I, about my performance as well last week.
"The good thing was the determination was in the training all week and I had a good feeling about the match, not that we would definitely win, but that we would definitely put on a good show.
"We had a calmness and I thought Motherwell caused us very, very few problems and we saw the game out quite comfortably."
The win came at a cost for Hearts as Jamie Walker limped off just before Smith's strike.
"He's damaged his ankle," Levein said. "There's contact and a twist so I need to wait and see.
"He was really good at the start of the game and that's the frustrating thing, I see him gradually coming back to what I know he can do. He was really incisive with his running with the ball and his general play was excellent."
Motherwell boss Stephen Robinson admitted his team were second best.
"We didn't deserve anything out of the game," Robinson said. "We were too slow, too predictable, right from the off.
"Declan Gallagher was our best player and he's playing with a 39 degree temperature, a proper man, a real man. We didn't have enough men, enough leaders in the team."
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