The Dragons found some success with their call to drop Lachie Ilias for rookie Lykhan King-Togia but it was rival halfback Jarome Luai who had his fingerprints all over a match-defining first half on Saturday night.
Already down 10 points, Saints had their spirits broken on the stroke of halftime after Jaydn Su'A dived over the line to score what would have been the Dragons' third try.
But just before he hit the turf, the ball inexplicably dropped from the second-rower's grasp in the wet conditions.
Bula collected the footy and sprinted from the in-goal to score under the posts just before the siren sounded.
In a flash, the Dragons went from what could have been four points down had Su'A scored, to 16 points in arrears.
"Obviously what happened just before halftime ended up being the turning point," said Dragons coach Shane Flanagan.
"It would've been 20-16, but it wasn't to be."
The bizarre turn of events proved pivotal to the end result when the Dragons fought back in the second half.
Bench hooker Jacob Liddle crossed for two tries and closed the deficit to one score, continuing his excellent season to date.
Bula's miracle try also came after he was left struggling to run when his ankle twisted awkwardly in a tackle from Clint Gutherson and Val Holmes.
The sides traded four-pointers in the final 10 minutes as Adam Doueihi and then Dragons forward Hamish Stewart crashed over but the Tigers never gave up their lead.
"I loved in the second half that we showed some grit to come back and get them," Flanagan said.
"We had opportunities to nail it at the back end and we just didn't do it."
Tigers coach Benji Marshall was reticent to even talk about the pivotal Bula try.
"I'm a little bit angry and happy at the same time, because he (Su'A) should've scored. For Jahream to pick it up and keep playing, you've got to make your own luck sometimes," he said.
"I don't want to sound like I'm negative about winning but there's just so many things we can do better."
Replacing the axed Ilias at halfback, teenager King-Togia looked the goods early in his fifth NRL game, sending a flat pass to put Dylan Egan over for the game's first points.
He blew the Dragons' next set in the red zone sending a no-look flick pass straight to Tigers winger Charlie Staines but put Liddle in for his second try.
Flanagan said "of course" King-Togia would be given more than just one game to prove himself as a first-grade half.
"He did a good job," Flanagan said.
King-Togia now has the same number of try assists for the season as Ilias managed in seven games, according to the NRL website.
Four-time premiership-winner Luai continued to push his NSW State of Origin case laying on two tries in the space of three first-half minutes.
He put a kick on to the left side that Doueihi fielded uncontested, passing the ball left for Staines, who confirmed a tryscoring double.
After a penalty in the set after points, the Tigers marched up the other end where Luai threaded a grubber kick past the line for Samuela Fainu to score.
The result means that if highly-fancied Canterbury beat Gold Coast on Sunday, the Dragons will finish the weekend as the only side never to have won at Magic Round.
Tigers centre Brent Naden left the contest early in the second half with a knee injury, with Dragons forward Emre Guler joining him on the sidelines with a shoulder problem later on.
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