It’s a clever idea but one that would mark the end of Yahoo(YHOO) as a brand. Mayer knows this. And during a conference call with investors on Tuesday, she responded strongly to Starboard — effectively telling them to ‘back off.’ Still, Mayer could actually use Starboard’s aggressive stance to her advantage if she plays her cards right. Here’s how:

Starboard’s suggestion of merging with AOL (AOL) is smart and correct. Yahoo has stuck to its core business of digital advertising even though the company has been floundering on that front for a while. What it needs is a technological partner that can update its old-fashioned digital advertising platform. AOL, by contrast, has ramped up its ability to deliver compelling video and mobile advertising, and could be a good partner for Yahoo. As proof of its superior product, AOL’s advertising revenues were up 20% in the second quarter this year while Yahoo’s fell by 8%.

What Mayer should do is buy AOL outright.

With a $6.3 billion windfall after taxes from the sale of its shares in the recent Alibaba (BABA) IPO, Yahoo is cash rich and can afford to acquire AOL, which has a market cap of approximately $3.5 billion. The cutting edge advertising delivery platform that AOL brings to the table will not only make the purchase accretive from a profitability standpoint, but it will enable Yahoo to strengthen and preserve its core brand. That is immensely valuable and even necessary for Yahoo.

Where Mayer needs to reject Starboard’s recommendations (and seems that she is willing to) is in the sale of its Alibaba stock and Asian assets. Those assets, as Starboard admits, have tremendous potential. And that’s exactly why Yahoo should hold on to them. The only apparent reason for the spin off at this time would be to realize tax savings, but that should not be the driver for breaking up a well-known brand that could generate immense value for shareholders in the future if it gets its knitting right – and with AOL under its belt, Yahoo might be able to do exactly that.

The other reason for Mayer to resist Starboard’s pressures to break Yahoo up is that the activist fund’s primary motivation to break up Yahoo is not to save the company but to generate immediate cash for shareholders. There is nothing wrong with this, of course. Jeffrey Smith, who runs Starboard, is in the business of maximizing shareholder wealth in the short-term. But Mayer’s job is to create value in the long-term, and in the Starboard version of this deal, she may have to give up the growth strategy that could be key to Yahoo’s success.

Mayer, who comes from Google, has pursued the same growth strategy for Yahoo as her former employer, trying to build the company through opportunistic acquisitions. The market reaction has been less than kind, and the CEO has frequently found herself under attack by analysts, particularly on the company’s $1.1 billion acquisition of blogging platform Tumblr in 2013.

However, despite the criticism, it seems that Yahoo’s biggest acquisition to date was a good bet, as Mayer announced Tuesday that Tumblr will bring in more than $100 million of revenues in 2015 from sponsored advertising and a rapidly growing user base. What this implies is that Mayer is not necessarily on the wrong track, even if the process is messy and comes with risks. She should stick to her guns even if others don’t share her vision.

This is a seminal moment for Mayer, who needs to show the market that she has the chops to lead Yahoo to higher profits in an uncertain time. She can do that by pursuing the acquisition of AOL while simultaneously ignoring the rest of Starboard’s recommendations.

Now that would be a power move.

Sanjay Sanghoee is a political and business commentator. He has worked at investment banks Lazard Freres and Dresdner Kleinwort Wasserstein, as well as at hedge fund Ramius. He does not own shares of Yahoo or AOL.