Messi put Barcelona ahead for good when he slotted in a pass from Cristian Tello after he had started the move by playing Tello wide.
Messi said Villa, who didn't play against Milan and hasn't played much this season, helped him in attack.
"Against Milan we didn't create many chances," Messi said. "Today, with Villa as a reference up front, their defenders had to stay put and that opened up spaces for me behind."
Sevilla also has a critical second leg in the cup on Wednesday when it must overturn a 2-1 loss to Atletico to earn a spot in the final.
After Tuesday's Cup semifinal, Madrid will host Barcelona in the Spanish league on Saturday.
Kaka was in Madrid's starting lineup only because coach Jose Mourinho rested several players, including top scorer Cristiano Ronaldo, for the looming trip to Barcelona.
The move almost backfired when Deportivo striker Ivan "Riki" Sanchez took a well-struck goal in the 32nd.
Desperate for a win in the home debut of Fernando Vazquez, its third coach in this strife-filled season, Deportivo outplayed Madrid in all facets during the first 45 minutes.
But after leaving Madrid without a shot between the posts until Jose Callejon's try in the final seconds of the first half, even Deportivo's best effort wasn't enough compared to Madrid's talent and two moments of inspiration from Kaka.
Banished to the bench for the better part of the last two seasons, Kaka said the playing time he was getting with Madrid out of contention for the league title was helping him recover his form.
"I'm feeling much better," said Kaka. "My coach needs me and I have to be playing well for the crucial part of the season."
The former world player of the year came through late when Deportivo's legs had grown heavy to give Madrid just its second win at Riazor Stadium in 20 years.
Ronaldo went on for Madrid in the 57th, but it fell to the little-used Kaka to level in the 73rd with an exquisite long-range strike reminiscent of his glory days at Milan.
Kaka then played Ronaldo clear in the 88th for the Portugal forward to cross to the unmarked Higuain who just had to push the ball home to prevent Madrid from slipping up again on the road.
Madrid forward Angel Di Maria was sent off in stoppage time.
Elsewhere, Jonas scored a double to secure Valencia a 2-2 draw at 10-man Real Zaragoza and lift the team into fifth place, while Getafe rallied for a 3-1 win at relegation-threatened Mallorca.
