Former Arsenal midfielder Watt scored twice in the first half, including the vital strike in added time just when Carlisle seemed to be establishing themselves in the game.
Dunne said: "Sanchez has speed over the ground and is a quality player and there is a lot more to come. He was aggrieved when I took him off because he wanted his hat-trick, but it's a team game.
"Sanchez scored a great goal in our first attack. The game plan was to get the ball out to him. The goal just before half-time was crucial.
"We wanted to be tough and resilient and go on to win and we did that brilliantly. Their goal was pure sloppiness. We need to be intense and we played more robustly in the second half when I felt we could hit them on the counter where we had the ability to score.
"We are winning games and scoring goals and moving in the right direction. We've played better and lost, but it's important to get the buzz of winning and there's that buzz in the changing room right now. We've hit Carlisle with sucker punches and kept our away record going and scored four goals and it's a great day for us."
A Magnus Okuonghae own-goal kept Carlisle level until just before the break, but Marcus Bean extended the U's lead with a header midway through the second half and a Max Ehmer own-goal put the result beyond question.
Carlisle scored an injury-time consolation goal through Ehmer who followed up after Sam Walker was unable to hold a Tom Lawrence free-kick,
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