• Microsoft shares closed up for the eighth day in a row, a feat not performed since January 2021.
• Analysts pointed to benefits stemming from updates at strategic partner OpenAI that were announced Monday.

Microsoft ended Tuesday's trading session at a record high of $360.53, following fresh optimism about growth from a key partner in artificial intelligence. The 1.12% daily increase gives the software maker a market value of about $2.68 trillion.

The major U.S. indices all posted gains for the day, with the S&P 500 notching its seventh-consecutive rise, while Microsoft delivered its eighth. The stock hadn't been on such a streak since January 2021.

At an event in San Francisco on Monday, Microsoft's strategic AI partner, OpenAI, announced a slew of updates, including price cuts and plans to allow people to make custom versions of the ChatGPT chatbot. Microsoft CEO Satya Nadella was on hand for the affair, and he emphasized that developers building applications with OpenAI's tools could get to market quickly by deploying their software on Microsoft's Azure cloud infrastructure.

Microsoft has invested a reported $13 billion in OpenAI, which has granted Microsoft an exclusive license on OpenAI's GPT-4 large language model that can generate human-like prose in response to a few words of text. Last week, Microsoft announced the release of an AI add-on for its Office productivity app subscriptions and an assistant in Windows 11, both of which rely on OpenAI models.

"What is good for OpenAI is good for Azure in our view," UBS analysts led by Karl Keirstead wrote in a note distributed to clients Monday. "If OpenAI is now actively courting software developers to build apps using ChatGPT/GPT-4, lowering price points and improving model performance, it could drive greater OpenAI consumption of Azure and serve as a modest positive for Microsoft." The analysts have a buy rating on Microsoft stock.

Oppenheimer analysts, with the equivalent of a buy rating, said OpenAI's price updates confirm OpenAI's status as the category leader.

When OpenAI succeeds, it's "mutually synergistic" for Microsoft, they wrote. Microsoft said in a regulatory filing in October that OpenAI is its "strategic partner" on AI.

Also on Tuesday, cloud monitoring software maker Datadog indicated to investors that its clients are starting to ease up on cost-saving projects. Datadog can monitor infrastructure in Azure and other public clouds, such as Amazon Web Services. Amazon ended the day up 2.13% but has yet to exceed its record close from July 2021.

WATCH: 2024 is the year of AI revenue, analyst says

Don't miss these stories from CNBC PRO:

• 75% of Warren Buffett's equity portfolio is in just 5 stocks. Here's what they are
• These two banks just hiked their 1-year CD yield to 5.3%
• A prudent way to bet on a bounce in Apple following its post-earnings decline
• Stifel says the S&P 500 will keep climbing 'wall of worry' to hit 4,400, gives 10 stocks to play rally