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Paul Stirling hits 65 not out
Andrew Balbirnie out for 37
Gareth Delany takes 3-16
Brandon King top scores for West Indies with 62 not out
West Indies won the toss and decided to bat first
Mayers & Charles out early
Evin Lewis caught first over after drinks break
Both sides have won one and lost one
Winner will advance to Super 12 stage
Scotland face Zimbabwe in other final Group B game at 09:00 BST
A completely dominant win for Ireland to secure their place in the Super 12s, following Sri Lanka and the Netherlands who qualified yesterday.
You can read Stephan Shemilt's match report here.
But that's not the end of the action - we will be back shortly for the next knockout game. Can Scotland join Ireland in progressing or will it be Zimbabwe?
That starts at 9:00, so please join us then!
Ireland captain Andy Balbirnie: "This means everything to us. We were so disappointed to miss out at this stage last year, so we had to do a lot of thinking and make a lot of changes back home.
"We set out some things we wanted to achieve as a team and how we wanted to play. And here, we lost our first game but to then come back and beat two-time champions in a must-win game, I could not be prouder.
"It was an emotional finish, we are absolutely delighted.
"A lot of things can happen in T20 cricket when it's your day, we want to test ourselves against the best in the world and who knows where that can take us?
"Paul is one of our best ever batters. The way he played today made it a lot easier for me and then Lorcan came in and played with real freedom. It is a really proud day for Ireland."
West Indies captain Nicholas Pooran: "It's really tough. We haven't batted well enough throughout the tournament and on a really good batting surface, 145 was always going to be a really tough challenge to ask our bowlers to defend.
"I want to say congratulations to Ireland, they batted and bowled fantastically today.
"There are positives to take, Brandon King is batting wonderfully and Alzarri Joseph always steps up for us with the ball which is nice to see. This is a learning experience for us, we are really disappointed and we know our fans will be disappointed back home.
"It's definitely hurting, I'm disappointed in myself and how it has gone but we will live to fight another day."
And let's get some reaction from the West Indies camp...
How good was Paul Stirling? He's not had the best year for Ireland but found his form just when they needed it.
Ireland's Gareth Delany: "It’s obviously an incredible day for us.
"This time last year were we were sitting around the dressing room after one of the toughest days so to get over the line today, in the fashion that we did, is amazing.
"Our spin bowling coach Nathan Hauritz, who couldn't be here today unfortunately, he came up the plan to keep it simple and be more defensive. We knew had to be defensive, we knew they were going to come at us so we just held our time.
"It’s a dream come true and we are ecstatic as a group over what we can do over the next few weeks."
The headlines will go to Paul Stirling, with Lorcan Tucker and Andy Balbirnie also playing brilliant knocks, but the win was set up by the bowlers and Gareth Delany in particular.
He took 3-16 from his four overs to ensure West Indies could only reach 146.
Paul Stirling finishes unbeaten on 66 from 48 balls and Lorcan Tucker an eye-catching 45 not out from 35 balls.
Ireland made light work of a chase of 146 to reach the second round of the T20 World Cup for the first time since 2009.
Image source, BBC Sport
Daniel Norcross
BBC Test Match Special
It has been a brilliant performance from Ireland who have out played West Indies today.
Lorcan Tucker skips down the wicket and smashes Obed McCoy over cover for four and that seals a historic victory for Ireland!
They have absolutely thrashed the West Indies by nine wickets and the former champions are OUT of the World Cup!
Hugs and smiles all round for the Irish though, who are absolutely buzzing and rightly so. A brilliant, dominant performance.
No winning runs for Paul Stirling unless Lorcan Tucker blocks out the next four balls!
Scores are level...
Need 2 runs to win
Paul Stirling tries to get the three remaining runs in style, swinging hard, but just gets a single.
He will be on strike for the next over, though. Irish fans are dancing in the crowd and they need just two runs to win.
A single to Stirling, four runs to win.
An absolute gem of an innings from Paul Stirling.
Image source, BBC SportNeed 6 runs to win
Chants of 'Ireland! Ireland!' echo around Hobart. It has been an absolute thrashing from Ireland.
Brutal, even.
Oh, Paul Stirling. He swivels in his crease and ramps the ball over fine leg for four more.
10 runs to win.
Need 14 runs to win
Pure brutality from Lorcan Tucker, smashed over long-on for an enormous six!
What a gem of an innings this has been to support Stirling, he's on to 38 from 30 balls and less than 15 runs required now for Ireland.
How's this for a catch?
Unfortunately for West Indies, it was by a spectator in the crowd...
Need 22 runs to win
Down on one knee, slog swept for an authoritative six by Lorcan Tucker off Akeal Hosein. Ireland's batters have targeted the spinner from the start, going for 38 from his four overs.
Need 32 runs to win
It's all looking very easy for Ireland at the moment, ticking the runs off while barely breaking a sweat.
Meanwhile the Scottish players are watching on as they prepare for their knockout game after this.