But two sensational comebacks saw them twice edge into the lead, the second time by 39 points to 37 with just a couple of minutes left on the clock.
Up stepped Steenson though, and he had two bites at the cherry. His first penalty attempt fell short. However, Billy Twelvetrees' clearance didn't make touch and Gloucester were caught offside.
The Exeter fly half needed no second invitation, and kicked his fifth penalty of the half to snatch the lead.
Even then, Gloucester didn't throw in the towel. They reclaimed the restart and, hoping for a penalty for offside, Freddie Burns' drop goal was off target.
So, Nigel Davies' side found themselves in the unusual position of scoring five tries away from home and still finishing on the losing side.
It was a harsh way to finish the season for a team who battled their way back into the game after a slow start. In a way, it was a shame that one of the teams had to lose after such a pulsating encounter.
In the end, both teams got what they wanted - although Gloucester dearly desired the win. The Chiefs qualified for the Heineken Cup and Gloucester took fifth place in the table.
But, that's it for now. Gloucester can reflect on a season of great progress under Nigel Davies, but will also perhaps reflect on missed opportunities in 2012-13.
The challenge now is to build on the foundations laid over the past 11 months.
It was a gloriously sunny Devon afternoon as kick off approached although, as is often the case, a tricky wind swirled around the stadium.
The Chiefs were as announced as they sought to clinch Heineken Cup rugby for next season, while Dario Chistolini came in for Yann Thomas on the bench for Gloucester.
It was an emotional day for the home side, with a number of players making their final appearance for the team including Richard Baxter who led the side out.
It was a lively start by the home side, whereas Gloucester had an early scare as Sione Kalamafoni received lengthy treatment after what seemed to be a blow to the head before groggily returning to action.
Exeter were first to score after gaining territory as Gloucester conceded a free kick followed by a penalty.
Powerful ball carrying and neat offloading had Gloucester scrambling. Jason Shoemark made the incisive break, before finding Dean Mumm on his shoulder and the Australian international was over. Steenson converted for a dream start.
It was quickly a 10-0 lead as Freddie Burns was penalised for not clearing the tackle area, and Steenson confidently bisected the posts.
It was all Exeter as Gloucester struggled to get any possession and, although Trinder denied Mumm with a superb covering tackle, neat hands down the blindside saw Damian Welch power his way over in the corner for a 15-0 lead.
A tough start was made even more difficult as Kalamafoni was forced to leave the action as the conversion was missed, but Steenson rapidly made amends with another penalty for 18-0 after 18 minutes.
The first quarter had belonged to Exeter, with the home team running it from everywhere but Freddie Burns finally got Gloucester on the board with a penalty.
Then, at last, Gloucester showed what they can do with ball in hand. Turnover ball in the Gloucester 22 saw Dan Robson make good ground, before drawing the final man for Jonny May to sprint home for a classic try to lift the travelling support.
And it was turnover ball that led to a second from Gloucester. Burns made the initial break, then Lokotui took it on before offloading to Sharples who burned off Arscott to score under the posts. Burns' conversion made it 18-15.
The pace showed no sign of relenting. Gloucester looked stretched in defence, before Henry Trinder picked off an errant pass. The centre then turned two defenders inside out on his way to the line for a superb solo score. Burns added an easy conversion to give Gloucester the lead at 18-22.
However, Gloucester didn't take the restart cleanly and found themselves defending a number of five metre scrums.
A couple of penalties later, referee Greg Garner gave a penalty try and Steenson's conversion saw the home team lead 25-22 at half time.
It had been a breathless 40 minutes, and the eventual outcome was still anyone's guess.
Gloucester almost been blown away in the first quarter, but then unleashed their talented back line to stun the home crowd until the last gasp penalty try.
Both teams were seemingly relishing the opportunity to play open rugby, with the ball moved wide whenever possible. It was a great spectacle and even the countdown clock went into meltdown at one point!
It was everything to play for in the second half. If Gloucester could tighten up their set piece and first up tackling, this one was within their grasp.
It was first blood to the Chiefs though. Koree Britton was penalised for holding on in the tackle, and Steenson kicked a well judged penalty.
It was the young hooker's last contribution, as he was replaced by Darren Dawidiuk after a fine effort in the tight, but a welcome return for Dawidiuk after suspension.
It was still an incredibly open game, and more tries looked likely. However, it was the boot of Steenson again, opening up a 31-22 lead as Gloucester again held on in the tackle, before adding his fifth penalty on 57 minutes.
Gloucester still weren't done though. Murphy smashed his way into the Exeter 22, before Burns exploited the blindside and put Rob Cook over for the bonus point try. Burns added the extras to get Gloucester back to 34-29.
It was game on as the game went into the final quarter, and even more so when Burns slotted a 62nd minute penalty, before Steenson responded in kind four minutes later.
Gloucester turned the screw and the pack led the way. The catch and drive tactic was thwarted as they worked the corner, as was a 5 metre scrum.
However, good work around the fringes created a blindside to work with and Freddie Burns was able to dart over in the corner after a smart pass from Twelvetrees. The fly half then converted off the post.
Gloucester had hauled themselves up off the canvas, but there was one more twist in the tail.
Unfortunately for Gloucester, it saw the game swing Exeter's way.
|Exeter Chiefs Score Card|
|Gloucester Rugby Score Card|