Meanwhile, the English side have exited the competition with the defeat.
The Saints were 6-0 ahead in the opening ten minutes thanks to two Ryan Lamb penalties.
The Irish side got on the scoreboard soon after as Ronan O'Gara kicked a penalty of his own.
Northampton extended their lead after 16 minutes thanks to a penalty try. Lamb successfully kicked the conversion to make the score 13-3.
Another O'Gara penalty edged Munster closer, but a Lamb drop goal regained the home side their breathing space.
However, BJ Botha's try on 31 minutes, coupled with O'Gara's conversion, made the score 16-13 to the hosts.
Another O'Gara penalty levelled the scores on 38 minutes, but Lamb's own kick put the Saints 19-16 in front at half time.
Johne Murphy's try three minutes after the break, along with O'Gara's conversion, finally gave Munster the lead, while Simon Zebo added another try for the Irishmen to give them a 28-19 advantage.
A penalty try just before the hour, converted by Lamb, moved the Saints closer to their opponents, but two more O'Gara penalties slowly saw Munster move out of sight.
Lamb pulled a penalty back for Northampton before two more tries for Zebo, giving him his hattrick, saw Munster move past 50 points.
The home crowd were given something to shout about with two minutes to go as Scott Armstrong burst through to touch down, with Lamb kicking the conversion.