It's not an unusual event for a stronger player — or, let's say, a better endgame player — to outplay a weaker one from an equal endgame. But what does this "outplay" really mean? To simply play stronger?
I don't think this quite illustrates it sufficiently, since chess isn't a race — the two sides come into contact and fight with each other. One player finds a more proper course of action and more accurately anticipates his opponent's best ideas, while the opponent fails to find the best play, or plays in an entirely planless way. The failure to fully comprehend the position in all its details may not be evident on every move - an experienced chess player can make reasonable moves on general principles, and sometimes those moves will turn out to also be the best moves in the position — but eventually will add up to various inaccuracies, which will cause the game to slip away.
Here we will be seeing a very instructive example I cam across recently, from an old game between Siegbert Tarrasch and Frank Marshall in their 1905 match. While of course both players were world class in their day, Tarrasch was significantly stronger (he won the match 8-1), and in particular Marshall's strengths were located in another phase of the game — not the endgame. Thus Tarrasch outclasses Marshall. We will see how, specifically, this happened.
The rook and pawn endgame began with the following position:
It is worth noting that Marshall had just captured a rook on f8 from his rook on f1, and Tarrasch had recaptured on f8 with the king. Thus we can see that Tarrasch understood that centralizing the king was important, and the f-file was relatively meaningless at this point, something which Marshall apparently misunderstood.
Basically the position is about equal. Black has the open a-file (the doubled pawns are not really a disadvantage for him at all) but there is not much he can achieve with it, since the white pawn on a3 is solidly defended. The main problem white faces is that the pawn on d4 is blocking two of his pawns and provides Black a sort of small space advantage. However, this situation could be easily fixed. Before checking out how the game continued (and how Marshall ought to have played), think for yourself - what would you play here? You may find the answer to be a revelation...
It wasn't easy, but White managed to lose this equal, nearly symmetrical position with only rooks and pawns. This same thing happens every day, and games such as this repay close study.