Can company run a successful business through a Facebook page instead of having own website?

Having only a facebook page as your online presence may be a good option if: you are a small business, with only limited reach and want to keep your customers engaged, like a restaurant that gives offers/info on specials, etc.
plus, not having enough budget to put up a proper website (the costs to putting up a website are decreasing continuously and can be managed with a very small budget if you are clear what you want).
Or if you are an individual showcasing a portfolio, etc.
(similar requirements) It must be noted that investing in a website is a great option for: brand building (you convey a good reputation).
If you are clear on the objective of your website (this is very important - and probably the first question you need to answer when thinking on your online strategy) There are many pros to operating on Facebook but do you really want to build your entire communication structure within one company's garden? Do both, spend more time on Facebook if the metrics say you should - but never give up your independence and ability to move.

Website in todays modern world of Marketing, serves as backbone of the company. Do Not confuse, Facebook, as alternative of website, Facebook is one of the leading tools of social media marketing, it can generate, Leads, awareness of your product and services/Brand. If company is small and cannot effort a big website, a simple Blog in Word Press will do your work.

YES! Not just selling but many more.
Few to name from which I have seen my self.
A young Egyptian man turns from buying Photography Equipment from outside and selling them only through his Facebook page, to have an offline retail store, and recently became an authorized dealer for a known Brand.
Other examples for a girl making Birthday Cakes for kids, which runs her business entirely through a Facebook page.
Some go far than this, by using their Page as a website where people share experience about certain topic and Advertisers can pay for their images/posts to be added to the page.

Will get more business through own website .

i think no no no, its a platform for awareness

It depends on what platform your using for your company website. Firstly you can not run a business on facebook as per its policies. You can get leads / branding done. With clever strategies you can get a bigger reach than your own company website.