David Wotherspoon clinched a 1-0 win for Hibs over Dundee, while St Mirren also won and Aberdeen and Hearts shared a 1-1 draw.
Cup finalists Hibernian finished their league campaign with a 1-0 home win over Dundee.
Hearts endure a frustrating end to a difficult week as Jamie Hamill's late own goal means they draw at Aberdeen.
St Mirren ended with only their third away victory of the season in the SPL as they beat Kilmarnock 3-1 at Rugby Park.
Celtic defender Kelvin Wilson is tired after the longest season of his career but knows he'll not get enough time to recuperate in the summer.