Intercepting SharePoint's SaveButton action to decorate/replace saving logic. Tested on SP 2013 Foundation

SPDataFormCustomSaveLogic.aspx.cs

// On your page with SaveButton you could do the following trick 
// (in my case save button is added in DataFormWebPart's XSL markup):

SPContext itemContext;
DataFormWebPart dataForm; // from designer's code behind

void Page_Init(object sender, EventArgs e)
{
    // NOTE: by some reason ItemContexts of controls in DFWP are differ,
    // so only SaveButton's OnSaveHandler is invoked
    itemContext = dataForm.Controls
        .FindControlRecursive<SaveButton>().ItemContext;
}

void Page_Load(object sender, EventArgs e)
{
    if (itemContext.FormContext.FormMode == SPControlMode.New ||
        itemContext.FormContext.FormMode == SPControlMode.Edit)
    {
        itemContext.FormContext.OnSaveHandler += OnSaveHandler;
    }
}

void OnSaveHandler(object sender, EventArgs eventArgs)
{
    // TODO: Add your code before saving the item
    SaveButton.SaveItem(saveButton.ItemContext, false, string.Empty);
    // TODO: Add your code after saving the item
}

WebControlExtensions.cs

public static class WebControlExtensions
{
    public static TControl FindControlRecursive<TControl>
    (
        this ControlCollection controls
    ) where TControl : Control
    {
        if (controls != null)
        {
            foreach (Control control in controls)
            {
                var foundControl = control as TControl 
                    ?? control.Controls.FindControlRecursive();
                if (foundControl != null)
                {
                    return foundControl;
                }
            }
        }
        return null;
    }
}

WebControlExtensionsTests.cs

[TestFixture]
public class WebControlExtensionsTests
{
    [Test]
    public void FindControlRecursive_returns_first_sibling_by_default()
    {
        var root = new Control();
        var expected = new Button();
            
        root.Controls.Add(new Control());
        root.Controls.Add(expected);
        root.Controls.Add(new Button());
        root.Controls.Add(new Control());

        root.Controls.FindControlRecursive<Button>()
            .Should().BeSameAs(expected);
    }

    [Test]
    public void FindControlRecursive_returns_nested_before_sibling_by_default()
    {
        var root = new Control();
            
        var expected = new Button();

        root.Controls.Add(new Control());
        root.Controls[0].Controls.Add(expected);
        root.Controls.Add(new Button());
        root.Controls.Add(new Control());

        root.Controls.FindControlRecursive<Button>()
            .Should().Be(expected);
    }
}