Set 240 to win, Michael Klinger (53) and George Hankins (67) added 99 for Gloucestershire's second wicket.
Taylor then smashed 64 from just 36 balls before being out with the scores level, but the visitors sealed victory.
Luke Wright had earlier made 84 for Sussex, but was caught behind off the impressive Chris Liddle (5-52).
After Wright fell on 182-5, having earlier been aided by Laurie Evans' 48, Sussex's batsmen struggled, with only Jofra Archer (30) making any real impact on the scoreboard.
Both sides are now on three wins after seven matches, but Sussex have a point extra after their rain-ruined match against Middlesex.
They can still make the top three - and a place in one of the two quarter-finals if they beat Hampshire at Southampton on Wednesday and Surrey lose to Gloucestershire at Bristol.
Gloucestershire's Jack Taylor:
"I'm hitting the ball well at the moment and it was nice to get us over the line for a good victory. We've just been too inconsistent in this format but we played well today.
"We weren't sure what a good score was going to be but we bowled well, especially Chris Liddle, and then Michael Klinger and George Haskins set things up nicely for me and Ian Cockbain at the end.
"Although we can't reach the knockout stages it's important to keep playing good cricket, not least because a lot of the skills are used in T20. It's good practice for that."
Sussex head coach Mark Davis:
"It's incredibly frustrating because we have played a lot better in this format but we have twice got ourselves in good positions and not won either game.
"We thought we had a competitive score but we got ourselves into a good position and then kept losing wickets at crucial times. They then set the game up with the way Klinger and Haskins batted.
"If we win the last game we'll give ourselves a chance of making the knockout stages so there is still a lot to play for."

He accused the government of failing on its deficit target, debt target and welfare cap - while pledging more taxes, debt and borrowing.
"The verdict could not be clearer - the so-called long-term economic plan has failed," he said.
Mr Hammond said there were not enough high earners to fund Labour ambitions.
Single market access
Giving his response to Mr Hammond's first Autumn Statement as chancellor, Mr McDonnell said the government was "ill-prepared and ill-equipped" to face Brexit - "the greatest economic challenge of a generation".
"The chaotic Tory handling of Brexit threatens the future," he told MPs. "You must now do the right thing for British workers and businesses - you must insist on full, tariff-free access to the single market....
"If you stand up for British business and jobs in fighting for single market access, you will have our support."
Turning to the rest of the statement, Mr McDonnell claimed six million people were earning less than the living wage and accused the Conservatives of treating so-called Jams - those who are "just about managing" - as being an "electoral demographic", adding "to us they are our friends and the people we represent".
"If you really want to make a fair tax system as well, you can start by bringing back the 50p rate for the very richest in our country."
'Race to the bottom'
He said it was regrettable that the chancellor was still going ahead with some of the cuts to Universal Credits, accusing him of "betraying" working single parents who he claims are at least Â£2,300 worse off.
He called for additional support for the social care budget, stressing: "We now have 3.9 million people on NHS waiting lists ... Many of those are waiting in pain and they have got no relief today."
He described the scrapping of tenant and letting fees as "a victory for Labour campaigning", but said home ownership was still "a dream" for the under 25s because fewer houses had been built under the Conservatives since the 1920s.
He said the chancellor was "continuing a race to the bottom" on corporation tax, while continuing to cut public services and cut taxes for big businesses.
But in response, Mr Hammond said the top 1% of earners contribute 27% of the tax paid. "Unfortunately, there aren't enough of them to finance all your ambitions."
Jack Taylor's fourth One-Day Cup half-century of the season helped Gloucestershire to a six-wicket win over Sussex with eight balls to spare.
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Chancellor Philip Hammond's spending plans "offer no hope for the future" after six "wasted" years, his Labour counterpart John McDonnell has claimed.