Chelsea recorded their first Premier League clean sheet for nine months, since a 2-0 win against Brentford in January.
Although Alonso said he was “not obsessed” with keeping a clean sheet, his side, who had conceded a league-high 13 goals before kick-off, were keen to address that record after a much-improved 5-1 win over Bournemouth following the international break.
There had also been discussion about Chelsea being a “soft” team, particularly away from home in the north of England, having lost 19 of their previous 41 matches north of Luton over the past four years.
Last season, Chelsea lost 3-0 at Everton during Liam Rosenior’s five-match winless run, a sequence that ultimately cost him his job. The Blues had also won just one of their past nine matches at the Toffees.
This time, however, Everton managed just six shots, their fewest in a Premier League game since recording five against Arsenal last December.
Chelsea also conceded only one clear-cut opportunity and allowed their lowest expected goals against (xG) figure against top-flight opposition this season at 0.45.
They started with a back three of Josh Acheampong, Maxence Lacroix and Levi Colwill, while goalscorer Neto and Jorrel Hato, who provided the assist, operated as wing-backs.
The midfield pairing of Moises Caicedo, returning from international duty, and new signing Jordan Henderson also brought much-needed solidity and experience.
It was £117m club-record signing Morgan Rogers, however, who set the tone for a combative display, squaring up to Everton defender James Tarkowski during an eventful first half.
“We needed to show that we can win in this way,” Alonso added. “We looked solid, we played solidly, we were strong and we stayed in control.
“In the first half there were difficult periods with throw-ins, corners and pressure from Everton. You have to overcome those moments.
“In the Premier League it is very hard to have complete control in an away game, but you cannot lose your shape or your conviction.”