The result left Villa, who narrowly avoided relegation last season, fourth on a maximum six points from two games while promoted Fulham are rooted to the bottom with no points after a third successive defeat.
Villa boss Dean Smith was pleased with a performance which also saw his side keep a clean sheet for the first time in 27 away Premier League games since a 0-0 draw with West Bromwich Albion in January 2016.
"We scored some quality goals," he told Sky Sports.
"On top of all that, you have to find the balance in football, and that can be the desire to keep the ball out of the back of the net, and the players have found that at the moment.
"John McGinn being fit makes a massive difference. He's a fantastic player, and he was terrific tonight."
Villa displayed clinical finishing at Craven Cottage but their victory was made easier by continued shambolic defending from Fulham, who have conceded 10 goals in their opening three matches and look out of their depth in the top flight.
Grealish fired Villa ahead in the fourth minute when he took a simple pass from McGinn into his stride and drilled a low shot past goalkeeper Alphonse Areola from a tight angle.
Hourihane doubled their lead in the 15th after a lightning-quick move down the left flank as McGinn racked up another assist when he teed up the Ireland midfielder to sidefoot the ball into the bottom corner.
The match was over as a contest in the 48th minute when Villa's England centre back Mings ghosted into the penalty area and turned in a predictable cross from the left with Fulham's defenders positioned like statues.
The home team's manager Scott Parker rued their poor defending.
"I've stood in this position for the first three games and it's a common theme of what I'm saying. You can't give up goals like we are, I've highlighted it and we know where we are.
"It's tough to fix the defensive frailties. I went with a back five today just to maybe give us a bit more solidity and it didn't work obviously."