Rick's answer actually breaks the vertical stretching of content inside the tabcontrol. It can be improved to retain vertical stretching by using a two row grid instead of a StackPanel.
<TabControl.Template>
<ControlTemplate TargetType="TabControl">
<Grid>
<Grid.RowDefinitions>
<RowDefinition Height="Auto" />
<RowDefinition />
</Grid.RowDefinitions>
<ScrollViewer HorizontalScrollBarVisibility="Auto" VerticalScrollBarVisibility="Hidden" >
<TabPanel x:Name="HeaderPanel"
Panel.ZIndex ="1"
KeyboardNavigation.TabIndex="1"
Grid.Column="0"
Grid.Row="0"
Margin="2,2,2,0"
IsItemsHost="true"/>
</ScrollViewer>
<ContentPresenter x:Name="PART_SelectedContentHost"
SnapsToDevicePixels="{TemplateBinding SnapsToDevicePixels}"
Margin="{TemplateBinding Padding}"
ContentSource="SelectedContent" Grid.Row="1"/>
</Grid>
</ControlTemplate>
</TabControl.Template>
与恶龙缠斗过久,自身亦成为恶龙;凝视深渊过久,深渊将回以凝视…