Northampton booked their place in the Heineken Cup quarter-finals thanks to a hard-fought bonus-point win.
HEINEKEN CUP Pool Three
Northampton (5) 33:
Tries: Reihana 2, Cohen, Soden, Thompson
Cons: Drahm 4
Glasgow: (13) 23:
Tries: S Lamont, Beveridge
Cons: Parks 2
Pens: Parks 3
Glasgow were the better side in the first half and were 13-5 ahead at the break with a Sean Lamont interception try and two Dan Parks penalties.
But Saints were much improved in the second half and tries from Ben Cohen and Mark Soden put them in control.
Although Glasgow battled bravely, Bruce Reihana's second try and another from Steve Thompson sealed the victory.
The victory means that the Saints qualify as one of the leading runners-up although they may have to face group rivals Toulouse in the last eight.
Saints were expected to complete a simple win at Franklin's Gardens but they did not have it all their own way against a dogged and spirited Glasgow side.
Scotland fly-half Parks had an impressive game and gave his side a deserved lead with a penalty from 24 metres.
However Saints hit back almost immediately and Reihana crossed with a help of a superb pass from wing John Rudd.
Parks added another three points before Lamont increased Glasgow's lead when he grabbed a floated pass on his 22 and was able to run in unopposed.
The home crowd were stunned into silence although they were given a boost when Kenny Logan was sin-binned in the closing stages of the half for deliberate obstruction.
Saints coach Budge Pountney read the riot act at half time and his side responded in kind with a much-improved display after the break.
Ben Cohen crossed to reduce the deficit before number eight Mark Soden scored from close range to settle Saints nerves.
Parks kept Glasgow in the hunt with his third penalty but Reihana's well-worked second claimed the vital bonus point.
Skipper Steve Thompson, who scored the winning try in the away win over the Scarlets last week, got in on the act with an interception try which saw him running in from deep inside his own half.
Glasgow claimed a late consolation score through Graeme Beveridge but Northampton's victory was already confirmed.
Despite the win, Pountney believes his side have a lot of work to do if they are to progress in the competition.
"We did enough, but not much more," he said.
"Of course, I am relieved we managed to get the bonus point - however we will have to step up several notches.
"We expected Glasgow to make it hard for us, and they certainly did that."
Glasgow lock Joe Beardshaw hopes his side's impressive performance will boost the rest of their Celtic League campaign.
"We came here confident we could get something out of our European campaign and not bow out empty handed," he said.
"But in the first half we showed what we are capable of doing at this level.
"It was very frustrating to lose like this after being ahead at the half-way stage, but there were plenty of positives to take out of the game."
Northampton: Reihana; Rudd, Cohen, Stcherbina, Tucker; Grayson, Howard; Sturgess, Thompson (capt), Morris; Seely, Lord; Blowers, Fox, Soden.
Replacements: Richmond, Smith, Browne, Krige, Jones, Drahm, Vilk.
Glasgow: Howarth; Lamont, Craig, Morrison, Logan; Parks, Beveridge; Tkachuk, Bulloch, Kelly; Beardshaw, Turner; Mather, Wilson, Petrie (capt).
Replacements: Lawson, Prescott, Dearlove, Beattie, MacLure, Henderson, Millard.
Referee: N Whitehouse (WRFU)