Installation errors - Windows 8.1 features like .NET3.5

I have a program that requires .NET 3.5. When I run it on my Windows 8.1, I get a pop-up saying:

An app on your PC needs the following Windows feature:
.NET Framework 3.5 (includes .NET 2.0 and 3.0)
[Download and install the feature]

The "Download" link starts installation, which fails with Error code: 0x800F0906, and a link to generic-style advice like "check your Internet connection". I also tried:

• Installing from Windows Features dialog, but got the same error.
• Downloading and running dotnetfx35.exe - got redirected to the above and failed with the same error.

Following Corrupted Flash Update prevents Windows Update - DISM fails 0x800f0906, I tried running sfc /scannow and dism /online /cleanup-image /scanhealth, but neither fixed the issue or produced intelligible logs.

So, how do I install .NET 3.5 on Windows 8.1?

Following output from sfc, I turned to read c:\Windows\Logs\CBS\CBS.log. At the time of failure, I saw the following lines:

Failed to find package: Package_78_for_KB2966828~31bf3856ad364e35~amd64~~6.3.1.4 from the index with mapping index packages recently rebuilt,  [HRESULT = 0x800f090d - CBS_E_MISSING_PACKAGE_MAPPING_INDEX]
Failed to get WU category/updateID for package: Package_78_for_KB2966828~31bf3856ad364e35~amd64~~6.3.1.4 [HRESULT = 0x800f090d - CBS_E_MISSING_PACKAGE_MAPPING_INDEX]
Failed to get the category and update ID for package: Package_78_for_KB2966828~31bf3856ad364e35~amd64~~6.3.1.4, component: amd64_microsoft-windows-wpfcorecomp.resources_31bf3856ad364e35_6.3.9600.20708_en-us_a3b67b207d2057ab, file: PresentationHostDLL.dll.mui [HRESULT = 0x800f090d - CBS_E_MISSING_PACKAGE_MAPPING_INDEX]
Exec: Missing files are found during staging attempt but failed to download content from WU. [HRESULT = 0x800f090d - CBS_E_MISSING_PACKAGE_MAPPING_INDEX]

On a hunch, I uninstalled KB2966828 mentioned in the log, and voilà - installation works! I hope Windows Update will install it again if it's really important...