Much of the pre-match focus was on Mata after manager Jose Mourinho omitted the World-Cup winning Spaniard, along with David Luiz, from his matchday 18 for Saturday's 2-0 victory over Fulham.
Mourinho insists Mata does have a future at the club but has challenged him to adapt his game and the midfielder, restored to the starting XI at the County Ground, responded in impressive fashion with an industrious performance.
Having provided a defence-splitting pass for Fernando Torres minutes earlier, Mata came close to a goal himself but saw his shot parried into the path of his compatriot, who this time opened the scoring.
Substitute Ramires added a second soon after as the Blues did enough against a gutsy Swindon side.
"Obviously a lot has been made of the Mata situation because he's a high-profile player," said Holland, who also revealed Marko van Ginkel suffered a potentially serious knee injury and Ramires a hip problem.
"The message to all of our attacking players from Jose from day one has been they need to contribute offensively in terms of their production and of course they have to contribute out of possession and defend.
"That's been the challenge not just to Juan but all of our attacking players.
"In Juan's case, if you look at his performance here, he made Fernando's chance and was involved in the goal. Those two moments - goal-making and goal-scoring actions.
"And then in injury time he's conceded the final corner of the game supporting Ryan Bertrand in the left-back spot, which is how he was all night."
Holland added: "Tonight, for sure, we're very, very pleased with Juan's contribution with and without the ball."
Mourinho's desire to get all of Chelsea's attacking players to perform the 'ugly' side of the game is clear.
And asked whether there is no such thing as a luxury player at the London club, Holland replied: "I don't think there is these days, I really don't think there is.
"You can perhaps carry a luxury player in certain fixtures but not many and, for sure, when you get to the business end of major trophies, if you're playing Bayern Munich and Barcelona you need 10 players who can all contribute out of possession."
Sky Bet League One opponents Swindon could be proud of their display having merely been caught out by two clinical attacks by their Premier League visitors, although goalkeeper Wes Foderingham was in superb form.
They also saw a chance of their own chalked off shortly after half-time as Dany N'Guessan was correctly ruled marginally offside with a header, cutting short the celebrations of most of those inside a sold-out County Ground.
Robins boss Mark Cooper said: "I was pleased with our possession but just a bit disappointed we haven't really tested Chelsea enough.
"Second half we had a lot of possession, we had a couple of good headers, one of them disallowed, and it would have been interesting if one had gone in.
"I was just a bit frustrated we didn't create more than we did going forward but we have to remember who we're playing against.
"It would have been nice to get a goal and ask a few more questions towards the end but to do that against Chelsea you really have to be on top form.
"But fair play to the players, they applied themselves very well, their attitude was good and they passed the ball really well at times again."
Source: PA
Source: PA