Northampton (9) 42
Best, Ansbro, Reihana, Mayor
Connacht (6) 13
Ray Ofisa's try briefly gave Connacht a one-point advantage
The steady boot of Stephen Myler was the foundation for Northampton's win over Connacht at Franklin's Gardens in the European Challenge Cup.
The fly-half slotted six successive penalties before second-half tries from Neil Best, Joe Ansbro, Bruce Reihana and Chris Mayor tied up the win.
Connacht had claimed a short-lived lead just after the break through a Ray Ofisa try, but were soon pegged back.
The Saints will face either Saracens or Newcastle in the semi-finals.
Connacht's indiscipline severely reduced their chances of progressing to that next stage with Brian McGovern, Jonny O'Connor and Gavin Duffy all dispatched to the sin bin at points in the match.
Duffy's departure coincided with the visitors' late collapse as Northampton finally made their numerical advantage pay with four tries in the last 11 minutes.
Jim Mallinder's side will now hope they can continue the superb home form that has seen them collect 32 wins in their last 33 matches at Franklin's Gardens in their last-four clash.
Northampton director of rugby Jim Mallinder:
"Our scrum was huge. Euan Murray, in particular, is playing well.
"When you can put teams under pressure like that and pick up penalties from your scrum it is fantastic for field position and we are really pleased with that aspect.
"It was a little bit of a late show again. You've got to keep patience and keep working and trust your game plan and the fitness of the players and we did that and came through in the end."
Connacht flanker Jonny O'Connor:
"It was disappointing. We let ourselves down because, definitely, that's a game we could have won.
"We played some good rugby at times and in the first half a lot of the play was down in their half but unfortunately we didn't go the distance.
Foden, Diggin, Ansbro, Downey, Reihana, Myler, Dickson; Tonga'uiha, Hartley, Murray, Fernandez Lobbe, Kruger, Best, S. Gray, Wilson.
Replacements: Lawes for Fernandez Lobbe (50), Mayor for Downey (71), Everitt for Myler (75), Dickens for Dickson (70), Smith for Tonga'uiha (75), Sharman for Hartley (70), Easter for Murray (64).
Duffy, Carr, Matthews, Ta'auso, Bibo, Keatley, Murphy, Wilkinson, Cronin, Loughney, Browne, Farley, J. Muldoon, O'Connor, Ofisa, McGovern.
Replacements: Nathan for Matthews (24), Dunne for Ta'auso (76), O'Loughlin for Murphy (76), Flavin for Cronin (73), McGovern for Loughney (35), Swift for Ofisa (59), Rigney for McGovern (63).
McGovern (36), O'Connor (63), Duffy (70).
R Poite (RFU)