Having scored two goals on his debut last weekend against Wolves, many were questioning whether that was a one-off performance or whether he could carry his form on, and he certainly answered any critics today.
Even though Walcott crossed for Richarlison to double the lead on 31 minutes, Everton's advances left enough space for the visitors to be encouraged.
Everton aspire to be back in European competitions next year and that's where away trips become even more hard but the Toffees have completed good business this summer by drafting in the likes of Richarlison and Yerry Mina, the latter of whom Michael Owen told BetVictor he expects to make his debut on Saturday - and they will need the Colombia worldwide to immediately settle into the rigours of the Premier League.
Saints were much improved after the break and they finally found a route back into the game through Ings, who pounced on Mario Lemina's knockdown from a corner to turn the ball home and hand his side a lifeline. They will add serious quality when deemed ready for regular action.
Mark Hughes needs to find the right formula quickly or Saints could be facing a long, hard season in the Premier League.
This was new broom stuff and in there was another fine display and another goal for Richarlison, substituted...
Charlie Austin was Southampton's highest-scoring player last season with seven goals in all competitions but he lacked sharpness on Merseyside.
"The attacking players linked up brilliantly at times".
Everton host Southampton in their next league match on Saturday. "Two games, three goals is important for him, but the first goal from Theo was important as well".