The 2-0 win in a controversial Merseyside derby followed on from three points at home to Wolves last week and erased the memories of reverses at Stoke and, in particular, Tottenham.
Beating Wolves was significant in light of the fixtures to follow as, having now made the short trip to Goodison Park, Liverpool host Manchester United after the international break.
They can at least go into that game with renewed confidence after seeing off their determined nearest-neighbours, albeit with a little help from referee Martin Atkinson who inexplicably sent off young Toffees midfielder Jack Rodwell midway through the first half for a tackle on Luis Suarez which was barely a foul.
"The two victories we've had back-to-back after the defeats has shown the character of the team and depth of the squad we've got here," said Downing.
"We all want to do well and getting wins like this helps.
"We played some good stuff at times but the sending-off killed them a bit and made it very hard for them.
"I wasn't near it at the time. It happened that quick I didn't have a great view of it but at the time I thought it would be a yellow card.
"It's easy for me to say that but it was a tough decision for the referee.
"But we kept pressing and it paid off in the end. Credit to the lads because we managed to exploit it in the end."
For a long time Everton made light of their numerical disadvantage thanks to their impressive work-rate and organisation but had almost undid it all when Phil Jagielka brought down Suarez just before half-time.
Dirk Kuyt, scorer of five Merseyside derby goals, saw his penalty brilliantly saved by Tim Howard and it was not until the introduction of Craig Bellamy and, to a lesser extent, Steven Gerrard, with a quarter of the match remaining that things turned in the visitors' favour.
Bellamy sent Jose Enrique away down the left and his cross, which Kuyt cleverly ducked under, allowed Andy Carroll to fire home his first Barclays Premier League goal of the season.
Nine minutes from time Suarez, who appeared to be targeted by bottles and coins thrown by Everton fans, clinched victory after Sylvain Distin's clearance rebounded off the Uruguay international's chest and dropped at his feet six yards out.
"It was a great game to be involved in. It was a great atmosphere and both sets of fans got right behind their teams," said Downing, one of five Merseyside debutants in the Liverpool side.
"It was quite feisty for half an hour, the tackles were flying in but that's part of the game."
Everton manager David Moyes was adamant Atkinson got it badly wrong with a decision which had a detrimental effect on the game.
"When it was 11 v 11 I didn't think it was a bad game," said the Scot.
"We had our fair share but the game nearly stopped at that moment (of the sending-off). It was in the players' minds."
Moyes attached absolutely no blame to 20-year-old Rodwell, who was distraught at the decision and left the field with some words of consolation from Reds midfielder Charlie Adam.
"Jack is a young boy making his way in the game so what footballer wouldn't have been disappointed.it was a big day for him," he added.
"He had a terrific tackle on Kuyt on the touchline just before that and we were in there competing with Liverpool, which is what we always try to do."