A new ad rollout by Twitter (TWTR) that allows advertisers to target mobile users based on how engage online on their desktops is already being heralded as an innovative approach — one that is catching Facebook (FB) off-guard.

Twitter’s ad concept aims to show users ads on mobile and desktop devices that are specifically tailored to them based on their cookies — basically areas that they’ve surfed and ads that may dovetail to their interests.

Twitter now will be able to track users across devices — something that Facebook has already been able to do some time.

At the same time, FB only has taken advantage of targeting ads to users who has visited that advertiser’s particular site.

Facebook’s slow march has allowed Twitter — and Google (GOOG) is doing it as well — to gain some traction against the still-unbroken FB social media dominance.

Because TWTR has seen what happens to FB when it constantly experiments with user privacy, it’s allowing users to simply opt out of targeted ads in their simple (compared to Facebook) privacy setting. Facebook’s more complex and hard-to-locate privacy settings have rankled users — and their eventual mobile retargeting efforts are likely to cause more blowback if they don’t ease into it.

Facebook turns a $2 billion revenue per quarter business — which is basically based on having ads on its platform.

The fact that Twitter is now taking advantage of a concept that Facebook came up with — but truly hasn’t taken advantage of — has reportedly caused the social network to rethink its own ad content.

Facebook now may have to come up with its own external ad network (via Business Insider). Right now, their ad targeting is limited.

The move has been a long time coming. Facebook currently sells advertising in two main ways: From clients who pay directly to run ads on Facebook based on Facebook’s own targeting data; and in an ad exchange named FBX that uses tracking cookies from other non-Facebook web sites to target users entering the site. Both methods have the same apparent result for consumers: ads show up on Facebook and in their mobile Facebook news feeds.

In the short term, TWTR is still in its ad-targeting infancy — which works to Facebook’s advantage if it moves fast.

The fact that Twitter is gaining traction overseas and with US users, however, means Facebook knows there’s a limited amount of time it has to pull ahead and keep TWTR from stealing its business.

Its something FB should have already been doing much quicker — a chink in the armor that Twitter is now exploiting.

FB stock is up 22% year to date.

TWTR stock is up 16% since its initial offering.