Ancelotti had made a change to the criticised midfield of Monday's defeat at Tottenham, with academy graduate Anthony Gordon replacing Gylfi Sigurdsson - the one player singled out for extra scrutiny against Spurs - and the youngster responded by being Everton's best player in the opening 45 minutes.
The Toffees' defence has been especially impressive, conceding only twice in that quartet of matches.
Following a 2-1 home loss to Everton on November 9, Southampton (13-4-16) sat a dismal 2-2-8 and the thought of possible relegation was not a far cry. The Toffees are unbeaten in nine top-flight matches at Goodison Park.
"We still have a chance to qualify for the Europa League.it will be really important to win our three home games". They have won their last two consecutive league games against Manchester City and Watford respectively.
The score draw leaves Everton and Southampton stuck on 11th and 12th on the EPL table respectively with one point separating the two teams.
The Saints stunned former Premier League champions Manchester City 1-0 at St Mary's in their last outing on Sunday. In truth, the team from the south coast were fortunate to gain the win, although they did work hard defensively.
The Saints have been risky on the road, as they have won six of their last eight away games in the Premier League, including at Norwich and Watford in their last two league matches on their travels.
Danny Ings has burst out of the break in fine form, hitting three goals in those four games as he continues to stake his claim for the Golden Boot.
With that in mind, there are likely to be plenty of punters willing to use the William Hill sign-up bonus to back Everton at generous odds of 23/20 to win this evening.