The sides were locked at 3-3 going into the break but following an early second-half penalty from Connacht's Craig Ronaldson, the rest of the game belonged to Ospreys.
Both Jeff Hassler and Martin Roberts touched down for the home side and although Eoin McKeon grabbed a consolation try for the Irish side, Ospreys triumphed 26-11 for their seventh consecutive GUINNESS PRO12 win.
Tandy's men are the only undefeated side left in the league but now have a break of three weeks before travelling to Ulster where they will try to preserve that record.
The victory over sixth-placed Connacht was the perfect response to last weekend's European loss to Northampton and Tandy credited his troops for their resilience after a trying week.
"I am more than pleased with that," said Tandy. "It was an outstanding result given the week we have had with international call-ups, off the back of a defeat against Northampton and bringing people in on loan.
"We have had some young players in and around the environment who have not had an extended period of game time and they showed up.
"We showed the players some footage at half-time where we thought we were doing a bit too much and not sticking to what we had spoken about.
"The boys have taken that on board and that is where those couple of tries in the second half have come from."
Click here for the best images from Osprey's triumph over Connacht
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