If Arsenal can keep this level of performance up they might still be capable of producing a miracle as they bossed Everton from start to finish with Welbeck opening the scoring after just seven minutes.
He brilliantly combined with Alexis Sanchez to jinx through the home defence before rounding Joel Robles for the opener.
Wenger’s delighted touchline celebration showed his relief while his side showed plenty of steel and confidence to keep Everton on the back foot.
The Toffees were too slow and flat and lacked the flair needed to threaten David Ospina’s goalmouth on a regular basis.
And just before the break Iwobi twisted the knife as he finished off another cracking team move to make the rest of the Premier League sit up and listen.
Iwobi is only 19 but has flown through Arsenal’s academy with ease and had ice in his veins as he slid a low shot past Robles as Arsenal surged forwards.
The only downer for England is that he has decided to play internationally for Nigeria rather than for the Three Lions, who he represented at youth level.
Wenger added: “He’s humble and we hope he remains humble because there is still a lot to work on, but he is a great talent.”
After the restart Everton played three at the back as they tried to drag themselves back into the clash but Arsenal snuffed them out as the Toffees sticky home form continued.
And the inquest on Merseyside is sure to be loud and long as the wheels continue to fall off Everton’s Premier League season.
Captain Phil Jagielka said: “We have been trying to find a reason and fathom what goes on but unfortunately it has just not happened.
“We need to find momentum and confidence between now and the end of the season. We need to find some consistency.”
Everton (4-2-3-1): Robles 6; Coleman 6, Jagielka 6, Funes Mori 6, Baines 6; Besic 4 (Stones 46, 6), McCarthy 5; Cleverley 5, Barkley 6 (Deulofeu 73), Lennon 6; Lukaku 5
Subs not used: Howard, Kone, Niasse, Osman, Galloway.
UP NEXT: Manchester United (a), Premier League, Sunday April 3.
Arsenal (4-2-3-1): Ospina 6; Bellerin 7, Koscielny 7, Gabriel 7, Monreal 6; Coquelin 6, Elneny 7; Sanchez 7, Ozil 6 (Gibbs 74), Iwobi 7 (Chambers 86); Welbeck 8 (Giroud 75)
Subs: Macey, Mertesacker, Campbell, Walcott
UP NEXT: Watford (h), Premier League, Saturday, April 2
REFEREE: Mark Clattenburg 7
STAR PLAYER: ALEX IWOBI: Scored a cracker – one for the future.
STAR SHOCKER: MUHAMED BESIC: Went missing early on and never came back.
MATCH RATING: 3