Google shares rose more than two percent to a new high of $749.38 at the close of the Nasdaq exchange on Monday and continued to rise in after-hours trading.
The stock price has climbed steadily this year as the California-based company bolstered its positions in key Internet growth areas with its dominant search engine, Android mobile operating system, and YouTube video venue.
The shares got a boost from a Citigroup note advising investors that the Google stock price could "rise significantly in the 12 months ahead."
Citigroup raised its target for Google to $850 from $740, saying that concern was abating regarding the cost of the Motorola Mobility acquisition, making money from ads on smartphones or tablets, and competition from Facebook.
Google shares were $751.09 in after-hours trades on Monday.
Recent public comments by Facebook chief and co-founder Mark Zuckerberg were credited with easing investor concern about a threat to Google's dominance in online search by Facebook, possibly in a partnership with Microsoft.
Zuckerberg said during an on-stage interview at a TechCrunch Disrupt conference in San Francisco that the social network's spin on search was likely to be answering questions with input from people's networks of friends.
For example, getting insights about restaurants, shops, films and more from those whose opinions are trusted.
But Zuckerberg was emphatic that Facebook had no interest in building its own smartphone and said the company was opting to focus on ways to make its service available on any devices people want to use to link to the Internet.
Smartphones powered by Android or Apple software accounted for an unprecedented 85 percent of the global market in the second quarter of this year, industry tracker IDC reported last month.
"The mobile OS (operating system) market is now unquestionably a two-horse race due to the dominance of Android and iOS," IDC senior research analyst Kevin Restivo said in the firm's quarterly Mobile Phone Tracker report.
"There is still room for some mobile OS competitors to gain share, although such efforts will become increasingly difficult as smartphone penetration increases."
Google-backed Android accounted for a "commanding" 68.1 percent of all smartphones shipped in the three-month period; while BlackBerry and Symbian saw their shares slip to 4.8 and 4.4 percent respectively, according to IDC.
Google's Android mobile gadget operating system, which is free to device makers, is seen as a shrewd way to make it natural for people to use the firm's money-making products and services on smartphones or tablet computers.