Goals from Bertrand Traore, Kortney Hause and Anwar El Ghazi saw Villa cruise to their third victory in four matches despite playing most of the match a man down, after Tyrone Mings was sent-off.
Goalkeeper Emi Martinez denied Wilfried Zaha early on before the hosts took control with Traore opening the scoring in the fifth minute.
Mings then saw red after tangling twice with Zaha in quick succession but Villa remained on top with second half goals from Hause and El Ghazi setting up their first home win in five attempts.
Villa have now won eight out of 13 Premier League matches to start the season and kept four clean sheets in succession.
Smith said: "I wanted the Christmas present of a good performance and result and I certainly got one with that result and performance.
“We were indebted to Emi in the first minute with a good save.
“Our counter-attacking threat was there for all to see. I thought we created numerous good opportunities with the first goal and could have scored a few more.
“Unfortunately Tyrone got sent-off but I said to the players at half-time there's no other striker I'd want in the Premier League to play with 10 men.
“I thought Ollie Watkins was outstanding and the only thing missing from his performance was the goal.
“The lads really appreciate the work he puts in. He has hit the bar, hit the post and the goalkeeper has made good saves as well. He will be disappointed he hasn’t scored but can be happy with his performance.”
Mings was booked twice in quick succession late in the opening half and will now miss Monday’s trip to Chelsea.
Smith said: “I thought both yellow cards were very soft. I thought the first one was pathetic. He got attacked by Zaha and got booked for it.
“The second one it looked like he was fouled by Zaha before fouling him. But the referee had set his tolerance level and once they do that you get soft sendings-off.”