But Ralph Hasenhuttl introduced Sofiane Boufal at the interval, and it was the substitute's cross that was tapped home from close range by Danny Ings to restore parity five minutes into the restart.
With pressure mounting on him, Marco Silva made a double substitution which includes Iwobi coming on for Walcott.
Richarlison will have to wait for the chance to build on his south coast display for Everton, with the global break now kicking in.
However, Richarlison was able to divert a Djibril Sidibe cross towards goal and in with 15 minutes remaining, earning Everton their first Premier League away win of the season.
The attacker has been called up to the Brazil squad and Everton will be crossing their fingers that he comes back fit and well, as they prepare for a busy period at the end of November and throughout December.
It was Everton's first point on the road since the opening day draw against Crystal Palace.
They return to action following the global break by hosting bottom club Norwich City at home.