diff --git a/public/Install-DbaMaintenanceSolution.ps1 b/public/Install-DbaMaintenanceSolution.ps1
index b47c7942331..52d33ab9a65 100644
--- a/public/Install-DbaMaintenanceSolution.ps1
+++ b/public/Install-DbaMaintenanceSolution.ps1
@@ -456,8 +456,17 @@ function Install-DbaMaintenanceSolution {
         }
 
         foreach ($instance in $SqlInstance) {
+            # Connect-DbaInstance tells us whether it opened a connection for us. We must only close what we opened
+            # ourselves, because closing a connection of the caller takes their session with it. See #10554.
+            $isNewConnection = $false
+            $splatConnect = @{
+                SqlInstance              = $instance
+                SqlCredential            = $SqlCredential
+                NonPooledConnection      = $true
+                IsNewConnectionReference = [ref]$isNewConnection
+            }
             try {
-                $server = Connect-DbaInstance -SqlInstance $instance -SqlCredential $SqlCredential -NonPooledConnection
+                $server = Connect-DbaInstance @splatConnect
             } catch {
                 Stop-Function -Message "Error occurred while establishing connection to $instance" -Category ConnectionError -ErrorRecord $_ -Target $instance -Continue
             }
@@ -558,7 +567,9 @@ function Install-DbaMaintenanceSolution {
 
                 if ($Pscmdlet.ShouldProcess($instance, "Dropping all objects created by Ola's Maintenance Solution")) {
                     Write-ProgressHelper -ExcludePercent -Message "Dropping objects created by Ola's Maintenance Solution"
-                    $null = $db.Invoke($cleanupQuery)
+                    # Invoke-DbaQuery names the database instead of running on the connection of the caller, which
+                    # $db.Invoke() would leave in that database. This is how the installation below runs as well.
+                    $null = Invoke-DbaQuery -SqlInstance $server -Database $Database -Query $cleanupQuery -EnableException
                 }
 
                 # Remove Ola's Jobs
@@ -891,8 +902,10 @@ function Install-DbaMaintenanceSolution {
                 }
             }
 
-            # Close non-pooled connection as this is not done automatically. If it is a reused Server SMO, connection will be opened again automatically on next request.
-            $null = $server | Disconnect-DbaInstance
+            if ($isNewConnection) {
+                # Close non-pooled connection as this is not done automatically.
+                $null = $server | Disconnect-DbaInstance
+            }
         }
 
         Write-ProgressHelper -ExcludePercent -Message "Installation complete"
diff --git a/tests/Install-DbaMaintenanceSolution.Tests.ps1 b/tests/Install-DbaMaintenanceSolution.Tests.ps1
index 5c1c470f19f..a80d3955ec8 100644
--- a/tests/Install-DbaMaintenanceSolution.Tests.ps1
+++ b/tests/Install-DbaMaintenanceSolution.Tests.ps1
@@ -193,6 +193,43 @@ Describe $CommandName -Tag IntegrationTests {
         }
     }
 
+    Context "The connection of the caller is left alone (#10554)" {
+        BeforeAll {
+            $PSDefaultParameterValues["*-Dba*:EnableException"] = $true
+
+            $callerServer = Connect-DbaInstance -SqlInstance $TestConfig.InstanceMulti1 -NonPooledConnection
+            $null = $callerServer.ConnectionContext.ExecuteNonQuery("CREATE TABLE #dbatoolsci_marker (id INT)")
+
+            # ReplaceExisting takes the code path that drops the existing objects, jobs are left out so that no
+            # SQL Agent command touches the connection - those are separate commands, see #10555.
+            $splatInstall = @{
+                SqlInstance     = $callerServer
+                Database        = "tempdb"
+                BackupLocation  = "NUL"
+                ReplaceExisting = $true
+            }
+            $null = Install-DbaMaintenanceSolution @splatInstall
+
+            $PSDefaultParameterValues.Remove("*-Dba*:EnableException")
+        }
+
+        AfterAll {
+            $PSDefaultParameterValues["*-Dba*:EnableException"] = $true
+
+            $null = $callerServer | Disconnect-DbaInstance
+
+            $PSDefaultParameterValues.Remove("*-Dba*:EnableException")
+        }
+
+        It "leaves the connection open, so the session survives" {
+            { $callerServer.ConnectionContext.ExecuteScalar("SELECT COUNT(*) FROM #dbatoolsci_marker") } | Should -Not -Throw
+        }
+
+        It "leaves the connection in the database it was on" {
+            $callerServer.ConnectionContext.ExecuteScalar("SELECT DB_NAME()") | Should -Be "master"
+        }
+    }
+
     Context "Additional backup parameters all enabled" {
         AfterEach {
             Invoke-DbaQuery -SqlInstance $TestConfig.InstanceMulti2 -Query $jobStep.Command -NoExec -EnableException