The Gunners continued the momentum from Saturday's victory over Birmingham to sweep aside the challenge of the Ukrainians, who brought an impressive record to the Emirates Stadium and had taken maximum points from their first two Champions League ties.
However, Arsenal made them look ordinary, barely getting out of second gear as Alex Song was gifted an early goal following a terrible fumble by Shakhtar goalkeeper Andrei Pyatov.
In-form winger Samir Nasri smashed home his second goal in three days to make it 2-0 before the break, with fit-again captain Cesc Fabregas' penalty ending the game as a contest on the hour while Jack Wilshere and Marouane Chamakh completed the rout.
Croatia striker Eduardo, sold by Wenger during the summer, netted a fine consolation goal on the return to his former club with seven minutes left, which brought a round of applause from the home fans.
After losing to both West Brom and at leaders Chelsea, Wenger feels his men are now back on track as they focus on Sunday's domestic top-of-the-table clash at Eastlands.
"We have won our last two games now and that is important because we go into the Manchester City game with a good level of confidence and with some certainties in the way we want to behave," Wenger said.
"When you win 1-0 people think it's too difficult, when you win 5-1 people think it's too easy.
"We had a good team attitude and we had a very good technical level."
Fabregas had been out since mid-September with a hamstring problem, while Wilshere had a point to prove following his headline-grabbing red card on Saturday.
Wenger has been impressed by the pairing. He said: "I am convinced it works well together.
"Jack has a good maturity level. You never think he is 18 when he plays and overall they combined very well."
Wilshere could be set for another England call-up against France in next month's friendly at Wembley.
On the possibility of the 18-year-old being handed a first start, Wenger noted: "Without wanting to make headlines, it's difficult to say.
"If you ask me the reverse question, do you think he is not ready to play for England? It's hard to say no."
The Gunners boss, though, warned against over-expectation.
"We have to give him time and let him play - I know that's not easy for you and not your [media's] greatest strength."
There was a flashpoint involving Wilshere during the first half when a late challenge left Shakhtar midfielder Tomas Hubschman in a heap, but which only received a stern warning from Norwegian referee Svein Oddvar Moen.
Wenger said: "Sometimes when you get such a storm you want to go the other way, but what was important was that he just played football.
"Jack is a player with a good technical level, but as well is a player who doesn't hide from challenges, and that is a tremendous strength which you do not want to lose."