Twitter is actually a great prospecting tool, and these are people you should absolutely be engaging with as a brand. The key is to engage without coming off as spammy. Instead of "Buy our product now to solve your issue", try something friendly like, "Hey XYZ! We'd love to help you [solve problem]. Let us know how we can help!" or "We'd be happy to put you in touch with one of our experts on this topic. Let us know if you'd be interested in chatting."
In other words, as long as you're focused on providing value over pitching your products, your responses won't come off as spammy, and you'll not only be able to get more qualified prospects from Twitter, but you'll also grow a stronger and more lovable brand presence.