International Business Machines reported better-than-expected third-quarter earnings on Wednesday, taking a step toward rewriting its narrative after a bruising second quarter.

The company posted adjusted earnings of $2.95 a share, ahead of analysts' calls for $2.85. Revenue rose 4.7% from the prior year to $17.1 billion, surpassing the $16.8 billion Wall Street had anticipated. While that pace of growth marks a modest pickup sequentially, it remains far below the 9.5% growth delivered in the first quarter.

The gains were most pronounced in IBM's software segment, where revenue increased 8% to $7.8 billion, beating analysts' calls for $7.66 billion. Infrastructure revenue rose 4% to $3.71 billion, while consulting revenue was roughly flat at $5.34 billion.

IBM stock climbed 4.5% to $262.75 in after-hours trading Wednesday. Shares had ended the regular session up 4%.

It was a welcome reaction, given that investors have yet to shake off Big Blue's second-quarter results, which the company delivered a week early in the form of a rare pre-announcement. The stock sank 25% on July 14, the day of the announcement, and marked its worst trading session on record.

Since then, shares haven't staged much of a comeback. The stock remains down over 13% since the close on July 13, while the S&P 500 and Nasdaq Composite each have gained more than 3%.

After such a steep plunge, expectations were subdued. Daniel Morgan, senior portfolio manager at Synovus Trust, noted ahead of the report that finding a positive catalyst wouldn't be easy.

Beyond the second-quarter disappointment, Wall Street has a reason to temper its enthusiasm given IBM's persistent struggles with sluggish organic growth. To offset the slump, the company has been leaning on software acquisitions in recent years, notably through the purchases of Red Hat, HashiCorp, and Confluent.

Jefferies analyst Brent Thill characterized IBM's third quarter as a "show-me story." While he acknowledged the low bar set before the report, he argued that expectations had normalized after a second-quarter earnings miss driven by poor execution and delayed large mainframe deals.

IBM said Wednesday that around two-thirds of those delayed deals had closed in the third quarter. However, that didn't lead to an increase in revenue guidance; the company reaffirmed its annual outlook of 4% to 5% growth.

Management did, however, raise another part of its outlook. Citing "strong free cash flow" in the latest quarter, CEO Arvind Krishna said the company now expects annual free cash flow to increase by more than $1 billion from the prior year.

Ahead of the earnings release, Citi analyst Fatima Boolani wrote that while results should largely match investor expectations, IBM has room to redeem itself over the long run. The mainframe business, in particular, could stage a comeback in the fourth quarter, Boolani asserted.

While IBM's name is closely associated with mainframes -- the high-performance computers designed to handle massive volumes of data -- its enterprise business also includes artificial-intelligence orchestration tools, cloud-based software, and a consulting arm to implement the technology.

Third-quarter earnings may offer a bright spot for investors, but Morgan Stanley cautions that IBM will face higher revenue expectations and a tougher macro backdrop in the coming months. While the latest results "should be viewed as neutral to positive" as delayed deals finally land, "the setup thereafter is more challenging," analysts wrote.