Johann van Graan's Munster side kept up their unbeaten run early in the competition to lead Pool B with a thrilling 38-27 win over the Cardiff Blues on Monday night, while Leinster continued their exceptional march with another massive win over an Italian side, this time beating Zebre 63-8.
Munster may have been without the likes of CJ Stander on international duty but his replacement Gavin Coombes touched down to give Van Graan's team their third straight win in as many games in the new season.
Mike Willemse scored twice for Edinburgh and Nic Groom added a third try, but it wasn't enough to stop Richard Cockerill's side conceding another defeat at the hands of Connacht as the Irish side won a high-scoring evening game by 37-26.
Jaco van der Walt was spot on with the boot, but wasn't able to make inroads as Connacht were just too good on the night.
Marcell Coetzee's excellent run of form continued for Ulster as he added another try to his tally as last season's finalists kept up their unbeaten run, with the bruising Bok loose forward having scored in every one of the three games thus far.
Coetzee added a superb turnover to set up Eric O'Sullivan's score in the second half while Louis Ludik added a brace of tries as the Northern Irish side ran away with the game, finishing 40-17 winners at the Kingspan Stadium.
"Everyone is a superstar here," Ulster coach Dan McFarland said afterwards, clearly pleased with the win.
"You can't win games, you can't go through seasons, and expect to live off a couple of individuals, it doesn't work like that.
"The effort and the skill of the preparation that the team put in during the week, literally you can't get a performance at the weekend without that."
Glasgow Warriors went down 23-15 to Ospreys for their second defeat of the season with Danny Wilson (coach) believing his side learnt massive lessons from the game.
"I think we were so close on so many occasions, only to spill the ball and then be defending inside our own half," Wilson said.
"It's a very new group with some new combinations, so it might take some time. To go from being comfortable to coming away with nothing is disappointing. We'll take a lot of lessons from that game as a group, though."
In other games Leinster's 63-8 demolition of Zebre on Friday night only underlined the massive depth the club has while Scarlets won a tense battle 10-3 against Benetton in a game that was tense and brutal at times.
Leinster 63 Zebre 8
Benetton 3 Scarlets 10
Ospreys 23 Glasgow Warriors 15
Ulster 40 Dragons 17
Edinburgh 26 Connacht 37
Munster 38 Cardiff Blues 27