Single verb meaning "to become more interested" or "to let your attention be caught"

Is there is a single verb that describes the action of becoming more alert and attentive to something?

If a teacher were to rivet students with an engrossing story or if a passerby were to strike up a conversation with a preoccupied stranger sitting on a bench what would be a word for the action of the students or the stranger in letting their attention be engaged? We use the phrase "catch someones attention" to describe the action of the teacher or passerby, but we don't often describe the way the students or stranger lets themselves be distracted.

EXAMPLE: "So and so was sitting on a bench absorbed in her thoughts when she heard her friend's name mentioned in a nearby conversation and immediately ________ with curiosity."

I'm specifically looking for a word similar to straightened/perked/piqued, however these examples are insufficient for one reason or another. Although straightened captures the bodily gesture I am looking for it is too general of a word and neglects to signify curiosity. Perked signifies a cheerfulness or liveliness rather than a stimulation of interest. And piqued too frequently carries the connotation of irritation or resentment.

EDIT:

I find it necessary to add this clarification to my question now that I have observed the direction of the answers. As FumbleFingers pointed out, I have "unwittingly restricted the scope of possible answers" to a precise context, and I apologize for not originally providing the sentence in which I intend to use the word. I neglected to do so because I thought the context would be difficult to explain in a concise manner and wrongly assumed it would be unnecessary to the discovery of a suitable word.

The sentence belongs to a novel I am writing in which a building, named Mançion, is sentient. Madee, the so and so, grows up in this building and is its close companion. It communicates with her via telepathy. At this particular point in the story Madee is wandering around Mançion as is her regular wont for the past decade since the building has countless rooms of incomparable wonder and beauty. While she is wandering absentmindedly the building asks her if she is ready to go for a walk. Given how normal walks are for her, (and the fact that she is already on a walk) the question strikes her as peculiar and catches her attention. Understanding this context I am looking for a word that will express the way she alters from absentminded wandering to a rather calm curiosity. Most of the words that have already been suggested carry too much liveliness or energy in their implication, which is out of keeping with the mood of the scene and therefore why I cannot use them.

The actual sentence in which I will be using this word is as follows:

Madee _____ with curiosity and followed Mançion down a passageway that opened in the wall.

It is true that I have chosen to retain with curiosity in the sentence. I feel that the mood would not be conveyed as adequately without it. Perhaps I just assume that no word would capture the almost absentminded perking of attention while still conveying a hint of curiosity. I apologize for being so persnickety. It is more than likely that no word exists which precisely conforms to the definition I am seeking and I will merely have to satisfy myself with one of the answers that have been provided or adjust my sentence.

P.S. alwayslearning seems to have caught on to the gist of what I'm looking for.

After some consideration, my best suggestion is:

Stir verb

to move or cause (someone or something) to move after being still

Madee stirred with curiosity and followed Mançion down a passageway that opened in the wall.

In my mind, "stirred" is fitting because it has an appropriate definition, but also conjures an image of being awoken by an unseen actor.

Captivate verb

to attract and hold the attention of (someone) by being interesting, pretty, etc.

So and so was sitting on a bench absorbed in her thoughts when she heard her friend's name mentioned in a nearby conversation and [was] immediately captivated with curiosity.

Perhaps riveted serves.

"So and so was sitting on a bench absorbed in her thoughts when she heard her friend's name mentioned in a nearby conversation and immediately was riveted."

2.2 Direct (one's eyes or attention) intently.
‘all eyes were riveted on him’

Reference:
https://en.oxforddictionaries.com/definition/rivet