Graendal was heavily involved in a plan to capture Rand, with three other Chosen she didn't trust. Asmodean knew her hiding place and was at Rand's service.

Graendal had to find out, and very fast, what happened to Lanfear in Cairhien and what caused Rand to attack Rahvin. It was a matter of life and death. Graendal had to assess the risk the conspiracy of four had been exposed or betrayed, and if Rand was coming for each own of them in turn with Asmodean at his side, to eliminate all the four Chosen. It was vital to her - on her findings about Rand's next moves would depend whether it was time to abandon all her plans and flee into hiding.

Read the last Asmodean scene more carefully. It's extremely obvious Graendal could have no idea Asmodean would open that very door in this area of the palace. Asmodean bumped into her purely by accident (or ta'veren twist etc.) - himself had no idea a few seconds before he opened the door that he would be going that way. It's when he saw the door he think he might use a cup of wine... No one was hiding for him behind the door, Graendal was surprised by Asmodean's arrival.

What could stand behind a small door in a corridor, a door Asmodean thought might lead him to a pantry (if you wonder what a pantry is, look in TGS. Nynaeve went to Chadmar's pantry to find a servant, and order him to go fetch the palace's equivalent of Renee Harfor (in a scene that parallel what Graendal did in Caemlyn, perhaps not by coincidence if Brandon got that scene from RJ's notes...). That's what Asmodean was looking for: a servant's pantry, a room in a palace where servants on duty await calls, stocked with the basic stuff the masters might ask for and what is required to serve these things (and Asmodean was wrong: service isn't done this way in the palace. When the masters ask for something, orders are relayed to the kitchens).

That's also precisely what Graendal would have been looking for as she could not easily roam around and had to stay somewhere discreet, like the servant's quarters: someone who could bring to her Renee Harfor, so she could compel her to have all the servants under her command (who would soon serve Rand and his inner circle) report everything they hear, which Renee would report to Graendal. She had to put her hands on Renee, compelling only a random servant would not have worked - he or she would find out enough. Only Renee could order all the servants to contribute, and no one in the staff would question why Renee wants to know as much as she could about Rand! Did Graendal managed it? *shrugs*. It's not important. What we can surmise is that when on the spur of the moment Asmodean saw a servant's (ie: smaller) door and opened it, he surprised Graendal who took no chance and killed him with a small amount of balefire. It had to be really minimal, because Graendal couldn't know what Asmodean was doing minutes ago - removing more than seconds of his life could raise a massive alarm. As for attracking Rand with her channelling, don't forget Graendal can invert her weaves. It had to be balefire. Graendal could not risk entering a duel with Asmodean (which would all too fast have raised the alarm and bring reinforcements to Asmodean). It had to be something he just couldn't counter. She had only one chance to remove a player terribly dangerous to her, and then flee in case Rand or his channellers weren't far behind. She also couldn't risk Asmodean escaping her, for then her presence in Caemlyn was exposed and if Asmodean had not betrayed her location to Rand yet, she had just painted a huge target on her back....

Graendal basically acted on instinct of survival. She got surprised during a risky (but necessary) attempt to spy on Rand, and she did what she had to do to survive the encounter.

As for her presence in the palace and so close to Rand being "unlikely" or foolish, just consider she did the very same thing again in Illian, with Rand and many Asha'man going in and out of the rooms she was spying on (and had looted, on the same occasion)... Graendal is no coward and takes calculated risks whenever she has to.

Another "less purposeful" possibility is that Graendal came to the palace to meet with Ravhin - the plan to capture Rand in Illian required the four Chosen stayed in touch on a very regular basis (she also had a meeting with Moghedien planned later that day - so it might have been her day to make the tour of the people she wanted to meet), realizing fast something was very wrong, and deciding to find herself spies in the palace (or to visit the ones she already had near Rahvin to find out what was going on...).