Two methods to perform basic authorization to access a REST API which allows this

curl_basic_authorization.ps1

// Method 1
$securePassword = ConvertTo-SecureString $password -AsPlainText -Force
$cred = New-Object Management.Automation.PSCredential ($username, $securePassword)
Invoke-RestMethod $Uri -Credential $cred
Invoke-WebRequest -Uri $Uri -Method GET -Credential $cred

// Method 2
$base64AuthInfo = [Convert]::ToBase64String([Text.Encoding]::ASCII.GetBytes(("{0}:{1}" -f $username,$password)))
Invoke-RestMethod $Uri -Headers @{Authorization=("Basic {0}" -f $base64AuthInfo)}
Invoke-WebRequest -Uri $Uri -Method GET -Headers @{Authorization=("Basic {0}" -f $base64AuthInfo)}