Out of form allrounder Andre Russell was taken off the ground in a medicab after suffering a hamstring injury nine overs into the Stars' innings.
Russell hobbling out of the game and possibly the tournament seemed to sum up the sad state of a title defence that has never gained any momentum.
The Stars built a solid total with Kevin Pietersen (60 from 37) smashing seven fours and two sixes in a typically belligerent exhibition of strokeplay.
A groin strain then prevented him from taking the field at the start of Thunder's innings.
The Stars had got off to a rollicking start, thrashing 62 off the first six overs, with Glenn Maxwell smashing 34 off 22 balls and Luke Wright 25 off 12.
The innings, which finished in steady rain, fell away after Pietersen's dismissal, with the Stars losing 5-16 inside the last five overs as Thunder captain Shane Watson impressed with 3-23.
Thunder's openers then dashed to 38 after four overs but the fizz among the sellout crowd quickly evaporated as they then lost 3-5 before Morgan rebuilt the innings and raised the hopes of the 20,076-strong crowd.
Morgan put on 42 with Ben Roherer (20 off 19) and then added 83 in 7.1 overs with Pat Cummins (22 not out off 20) to steer them to the vital win.
Morgan described the sensation of hitting his last-ball six as "unbelievable".
"It's quite an extraordinary feeling when you get one as cleanly out of the middle as that," he said.
"It's a bit like standing on the (golf) tee box and smashing one straight down the middle. When you hit it, you're the only person who knows how well you've hit it."
Thunder officials said Russell iced his left hamstring from the time he came off the ground and would have a scan on Thursday to see if he would need surgery.
Pietersen said he didn't come out for the Thunder innings because he didn't want to field on a wet surface with a "little bit of a groin strain."
Asked what went wrong for the Stars, who now have a 1-2 record, Pietersen said: "'The last four of five overs of the batting wasn't special and we didn't start the bowling as well as we could have and then Eoin Morgan played really well.
"We tried real hard to lose that game and we did."
