Although the fixtures were just two days apart, Hughes opted to name the same starting XI for the clash with the Toffees as he had for the impressive 2-0 home victory over Manchester United on Boxing Day.
Arnautovic, who scored during a fine individual run-out that lasted the full 90 minutes against United, went on to produce more of the same at Goodison Park, setting up two goals before securing a dramatic 4-3 win with a stoppage-time penalty he had earned himself.
And Hughes said of the Austria forward: "Marko did great once again, but he was struggling before the game - I have to say, he was the one big gamble we had.
"I went with the same team and was happy enough with that - we had enough energy and I thought we could ride the wave of the Man United performance a little bit and see where it took us.
"Marko was probably the only one I had a real doubt over, but thankfully I went with a gut feeling and he has produced the goods again."
Arnautovic actually slipped as he took the penalty and Hughes admitted he had feared the worst.
The manager said: "I noticed almost immediately and thought 'here we go', because there have been a few penalties in recent weeks where the ground was sodden and people have missed.
"But thankfully Marko didn't and was still able to get good power on it."
Monday's thrilling encounter featured two major areas of debate, the first surrounding Stoke winger Xherdan Shaqiri's eye-catching effort to make it 2-1 just before the interval.
Shaqiri, who had already opened the scoring with a finish subsequently cancelled out by Romelu Lukaku, restored his side's lead by meeting Bojan Krkic's lofted ball to the edge of the area with a touch that sent it floating over the stranded Tim Howard and in.
Some observers have labelled it a fluke, but others have hailed it as a goal-of-the-season contender - while the Switzerland international himself, quoted by The Sentinel, insisted: "I knew what I wanted to do...does it look like I didn't!?"
The second hotly-debated incident - coming after Lukaku and Gerard Deulofeu had made it 3-2 to Everton and substitute Joselu had then drawn things level once more - was that which led to Arnautovic's penalty.
Referee Mark Clattenburg awarded the spot-kick having judged Arnautovic had been fouled by John Stones.
Everton boss Roberto Martinez later labelled the decision "terrible".
But he also conceded his side, now with only one win in six Barclays Premier League games, were not without blame for their downfall, particularly defensively.
Martinez refused to single out individuals for criticism, despite specific questioning about goalkeeper Tim Howard's performance, but said: "As a team, we need to be a bit wiser and learn quickly.
"I don't think we defended well enough or managed the game after going 3-2 up.
"That is clear, it is something we need to improve and it is where the work is
It is a recurrent theme.
"We need to get better in those situations
We often get in the lead, which is what we want, but now we have to make sure we know how to protect those leads."
Martinez also confirmed James McCarthy had departed the field having suffered a recurrence of his hip injury, while fellow midfielder Tom Cleverley is "a bigger concern" due to an Achilles problem that forced him off.
Source : PA
Source: PA