The Premier League title hopefuls were under pressure during spells in the first half but led courtesy of Oscar's strike just before the break.
Diego Costa then put the game beyond doubt with a second before the hour and the hosts were able to see the win out with relative ease at Stamford Bridge.
Assistant Holland - on press duties in Mourinho's place - felt words of wisdom from the Portuguese during the interval were key in ensuring a victory that saw Chelsea move two points clear at the top of the table, thanks in part to Manchester City's 1-1 draw with Everton.
"He's a highly experienced manager who knows what to say and when to say it. He wanted the team to play further up the pitch, press further up the pitch, to be mentally more aggressive and assertive with and without the ball," Holland explained.
"He wanted us to play at a quicker tempo and sustain attacks in their half. Our performance level has been very good and consistent this year. In the first half we dropped below that.
"Jose was very clear to the players at half-time with what they needed to do, and the performance in the second half was more like the Chelsea we're used to seeing week in, week out.
"It's very difficult to hit the levels people expect every week, particularly in this country because we play so many matches, especially at this time of year.
"The players have had a real battering over Christmas and to reach the level everybody wants to see week in, week out is almost impossible."
The only downside to Chelsea's win was an injury to Cesar Azpilicueta in the first half, which saw him replaced by Filipe Luis.
"He has a slight groin issue," Holland added.
"We don't think it's a major problem but we'll know more when they do the scans in the next few days."
