The Dutch emerged victorious from a slow-burning and often fractious contest in Sao Paulo, maintaining their 100 per cent record in the pool, after substitutes Leroy Fer and Memphis Depay both notched late goals.
It was a different performance to that Van Gaal's side had produced when they beat Spain 5-1 in their Group B opener or when they then saw off Australia 3-2.
And the Oranje boss, quoted on FIFA.com, said of the Chile encounter: "It was a match of the highest quality.
"We limited Chile to a handful of opportunities, we neutralised them extremely effectively - and particularly in the second half we created more chances.
"We did have to change our style today - and I will always pick a system and a strategy that will help us win.
"However, we're not perfect - in possession we still need to improve, but I do think we're very good without the ball."
After each winning their first two group matches, both sides had already qualified for the last 16 ahead of this contest.
But they went into it knowing that clinching first place in the pool would see them avoid a meeting in the next round with the winners of Group A - likely to be hosts and tournament favourites Brazil, who were in action later on Monday.
Goal difference meant Holland needed only a draw to ensure they remained at the summit.
And despite Van Gaal's comments about picking a team to win - and the fact that that was the final outcome - Chile coach Jorge Sampaoli suggested that the Dutch had "only wanted to defend".
Sampaoli said: "We kept going and fighting for 90 minutes, but ultimately we didn't get the result.
"We wanted to win this game and we gave our all.
"We felt that Netherlands only wanted to defend. We expected Netherlands to go on the counter-attack with regularity and for such a long time we limited them to long shots.
"I felt that our intensity and commitment was outstanding. Our players should have their heads held high as we've played well in the three games so far and we're now through to the round of 16."
Holland winger Arjen Robben - who, following Fer's 77th-minute header, provided the tee-up on the break in stoppage time from which Depay converted inside the six-yard box - said: "If you told me that we'd win our three games to finish top of the group two months ago I'd have been delighted, but I don't want to end it here.
"We want to go on. Although we want to enjoy the moment, we'll soon need to start to work hard in training to improve even more.
"You have to give compliment to both teams, both gave 100 per cent today.
"We defended really well - and although Chile finished second I think they go far in this tournament."