To answer this question, it is necessary to touch a few theoretical points. I will try to be brief.
The first distinction that it is important to make is between a drawish position and an equal position. The first refers to positions in which no side can really strive to win and the result is most probably a draw. The second refers to positions in which both sides have equal chances of winning. So yes, there are equal positions that are not drawish, and this already hints an answer to your question.
For a profesional player it is easy to reach both drawish or equal positions right of the opening. Depending on the player's spirit, as well as the tournament strategy he is using, whether he'll go for one or the other.
To go for equal positions instead of drawish positions, you need positions with imbalances. An imbalance is some strategical, positional or material factor that alters the equilibrium of the game in one way or another. They do not necessarily mean "disadvantage" or "advantage": an imbalance simply means each player has different things to play with.
For example, this is a balanced, drawish position:
The position is typical of the exchange variation of the French Defense. It is balanced because there is equal material, same pawn structure on both sides, same king safety, same central control, same development, same everything. Boring!
This is an imbalanced position. White claims greater space on the queenside (and therefore prospects of queenside play) and more space in the center, while Black can claim a potential attack on the White king and eventually more space on the kingside.
Both positions are equal. However, they aren't both balanced.
To finish, the way a GM can try to avoid drawish positions is to create imbalances. Some openings are more balanced than others. The exchange french is balanced and extremely drawish (and boring), while the Winawer french or the KID are imbalanced positions.
Due to the extreme ability of GMs, they more often than not reach draws even in imbalanced games. This is because both players know how to exploit their different advantages and defend their different weaknesses. However, the fact that they reach draws do not mean the games are drawish. If there are imbalances, there are winning chances. It's just that they are, more often than not, too good to lose.