The hosts were restricted to mainly long shots in the first half and went ahead when Sami Khedira's strike was deflected in.
Read how the action unfolded below.
6.47pmHello everyone and thanks for joining me tonight for coverage of this Group C qualifying clash between Germany and Republic of Ireland.
6.50pmGermany have brushed all aside so far in this group and a win tonight would put them through as group winners, which will see them join Italy and the Netherlands in the World Cup. So far they have dropped just two points - that bizarre 4-4 draw against Sweden almost a year ago.
6.54pmIreland have the slimmest of hopes of a playoff spot. They'll need Austria to beat Sweden and turn over a massive goal difference. Essentially, they're out and second is between the other two sides. It will most likely go to Sweden, who just need to avoid defeat to the Austrians.
6.58pmI'm sure you'll be delighted to hear that I have the team news. Coming right up... I don't think it's too much of a spoiler if I wish stand-in manager Noel King the very best of luck!
7pmGERMANY XI: Neuer; Lahm, Mertesacker, Boateng, Jansen; Khedira, Schweinsteiger; Kroos, Ozil, Schurrle; Muller
7.02pmIRELAND XI: Forde; Coleman, Delaney, Kelly, Clark; Whelan, Gibson, McCarthy, Wilson; Doyle, Stokes
7.06pmDo you see why I said good luck? It's not quite a full-strength Germany, but it is an XI that would cause most teams in world football huge problems. There is not Marco Reus, but never to worry - Andre Schurrle comes in. Joachim Low also opts for Thomas Muller as the striker instead of Miroslav Klose.
7.09pmMesut Ozil will be pulling the strings and I'm interested to see how Toni Kroos does - presumably he'll be in the middle with Ozil on the right, but there will probably be a lot of movement between the two of them.
7.13pmFor Ireland, Seamus Coleman captains the team and he has a big role to play tonight. He loves to bomb forwards and up against Marcell Jansen he might get some chances to cross. Jansen is no mug, of course, but he's not to Marcel Schmelzer's standard in my opinion. Anthony Stokes and Kevin Doyle start, which looks to be two up top for the Irish.
7.19pmOf course it won't be embarrassing for Ireland if they lose this one tonight. The qualifying campaign is a write-off but there are a number of players who will be looking to impress for inclusion in future squads.
7.23pmTo this point Germany have scored 28 goals in qualifying and I'd be surprised if they didn't get past 30 tonight. They have conceded seven, so they are fallible, but have markedly tightened up in recent games, which is the area Low has been focusing on lately. Four of those seven did come in the one game - one half, in fact - against Sweden last October.
7.27pmA look at the odds, if it was needed, tells us that Ireland basically don't have a hope. For the incredibly ambitious out there a £10 bet on the visitors would net you £180. A bet on Germany is equally pointless but for an entirely different reason - their odds of 2/11 don't represent the opportunity for much profit. A good inclusion in an accumulator, though.
7.30pmOf course the game is not played on paper and you just never know. Not many sides have survived an onslaught from this German team, however, and I think they'll be the team to beat in the summer. We're just 15 minutes away from kickoff now.
7.35pmWhat of the other teams in the group? Well Kazakhstan have four points and the Faroe Islands, as ever, have none.
7.38pmIt should be a good game here as there is still much to play for for Germany. They will want to win the group in front of what will be a noisy crowd in Cologne.
7.42pmAnthems and pleasantries being dealt with and we are almost set to get underway. Prediction, you say? I'm going for 4-1 to the Germans - and that's being reserved.
1 minkickoff: Here we go then, the hosts in white get us underway - Kroos and Ozil to be precise.
3 minLots of passing early on from Germany, as you might expect. Ozil and Muller have combined nicely on a couple of occasions but there have been no chances as yet.
6 minMuller is already drifting into the channels and is making himself very hard to mark. He moves to the left to claim the ball before finding Philipp Lahm. The right-back finds Ozil, who tries to curl one but it starts too far outside the post and goes wide.
9 minIreland won a corner a few moments away but nothing came from it. Germany attack immediately from it and win one of their own, but it's a good claim from Forde. Ireland have defended very well so far.
12 minGOAL! Germany 1-0 Ireland (Sami Khedira)
12 minAnd there's the first. High pressure won Germany the ball inside the Ireland half. It fell to Lahm, who played in Khedira and his shot took a huge deflection past Forde and into the net. That's unfortunate for the keeper, but it could not be a long night.
14 minIt was more a noise of expectation than a cheer from the German fans, but you can be sure that they are enjoying this so far. Jansen finds space down the left to cross but it's cleared well by Delaney.
18 minThis is being played at Germany's pace now. There is no need for them to force the issue and as usual every player is getting regular touches on the ball.
21 minThey are just upping the tempo a little more now as Schurrle drives at pace down the left. Kelly does well to block his cross for a corner but it's starting to look like just a matter of time as an ambitious Boateng shot is blocked behind for another one.
24 minCrosses are coming in from left, right, the byline and deep at the moment. How much longer can Ireland hold out? Not only that but they're behind so will want to see the other end of the pitch as well.
26 minBit ambitious for Kroos there. Lahm finds Ozil, who in turn looks for Kroos. He shapes to shoot on his left but turns and tries with his right from about 25 yards and it's blocked behind. I'm not sure it was threatening the goal.
29 minKroos goes for goal again and once more it's blocked behind. There have been more deflections in this game already than I can remember seeing in one. The good news for Ireland is that they are forcing the Germans to shoot from range.
31 minVery, very good tackle there from Khedira. McCarthy looked to threat Stokes through but the defensive midfielder had tracked him well and timed the slide to perfection. He really does get all over the pitch.
34 minSAVE: Jansen is almost playing as a left winger now. There's so little attacking threat from Ireland that they can afford an extra man going forward. On the right side, though, Lahm gets in a cross and Forde parries it away from Schurrle's header.
37 minSAVE! Another fine save from Forde. That one is really good indeed. Muller cuts from right into the middle and catches a shot superbly. It's arrowing towards the roof of the net and Forde gets a hand on it to tip over.
40 minCan Ireland survive to the break at 1-0? They'll be pleased with that and also happy that Germany haven't really carved them open. They've had plenty of shots, but most have come from outside the box - even the goal was from the edge of the area.
43 minIreland are just having a bit of possession here, although they are forced all the way back to Forde with some high pressing and Germany eventually win it back. Khedira then looks long for Schurrle, but Kelly reads it well.
45 minCHANCE! That is a chance, but Muller did not get enough contact on his left-footed effort. He was found by Ozil but rather scuffed his shot at Forde.
45+1 minHALF-TIME: Germany 1-0 Ireland
8.36pmIreland have given a good account of themselves in this half - mainly at the back. They struck the bar right at the end of the half from a free kick but aside from that it has been constant pressure.
8.40pmAs it stands Germany are about to go through as group winners. You would fancy them to win from here and aside from that late header have looked very comfortable at the back. Both full-backs have bombed forward, but the back two have been well protected by Khedira.
8.44pmBoth Ireland strikers have been isolated so far and really well marshalled by Boateng in particular. Of course it was going to be defensive stuff - most sides will have to against Germany - but Coleman will be disappointed how little he has been able to get forward. Jansen has pressed right up and penned him in.
8.48pmThe players are coming back out for the second half. I'll let you know if there have been any changes - certainly the Germany team looks like the same group.
46 minKICKOFF: The men in green get us back underway and Stokes puts a shot from just outside the box narrowly wide of the post! Great start.
47 minSAVE: Neuer is then forced to tip a cross over the bar. The team talk has really spurred up the Irish as McCarthy fires over after the corner was partially cleared.
50 minGermany have soaked up that early pressure and are now seeing a lot of the ball. A marvellous touch from Lahm there to control an angled ball from Schurrle, but he tried to cross instead of shoot and it was blocked behind.
52 minCHANCE! Oh dear Neuer! The keeper comes out to meet a punt forward but misses the ball. It's wide but all Stokes has to do from the byline is hit the target but he scoops the ball well over.
55 minI get the feeling Ireland have had their chance. They might well be level with their performance at the start of this half, but it will take one Germany goal and the points will be secure.
57 minBOOKING: Sweden, meanwhile, are level with Austria now. If it stays like that then Sweden will be into the playoffs. On the pitch, Schweinsteiger muscles in on Doyle but goes into the book as he brought him down.
58 minGOAL! Germany 2-0 Ireland (Andre Schurrle)
58 minLovely goal, but that's static defending from Ireland. They fail to track Schurrle's run from Kroos's dink over the top and he has time to control, turn and slot into the bottom corner. Game over.
60 minSAVE! Schweinsteiger doesn't half have a powerful shot. Again, though, Forde is across to put it behind for a corner. That must have hurt his wrists.
62 minBOOKING: Second card of the game and it goes to Stokes. He was beaten for pace by Jansen and had a hold of his shirt; an easy booking for the referee.
65 minNervy moment for Coleman as he picks up the ball after Jansen's cross was cut out. He's almost robbed by Schurrle, but does well to get away with the ball. A few seconds later it's a corner, however, as Kelly cuts out a pass into the box.
69 minThe movement in the attacking third is so great to watch for Germany. It's Ozil this time who's wide left, and he gets it back following an angled ball. He finds Jansen who clips in a cross but it's too high for anyone in white.
72 minCHANCE! That's a perfect pass for Muller from Jansen, who rakes an angled pass into the box. Muller arrives at the far post but having got there will wish he'd done better as he turned his effort wide.
75 minOuch! Delaney blocks a shot with his face and goes down briefly. It deflected possibly into his face via an arm, but he's straight up. Ireland enjoy a bit of possession in the middle but there's nowhere to go amid the white shirts.
78 minStill Germany look most likely to score again rather than concede, but there's not a great deal of urgency from either side at the moment. Smart foul from Jansen on Whelan, who brought him down to allow his teammates time to regroup. Stokes wins a corner off Boateng - they have threatened from set pieces so far.
81 minSAVE! Really nice footwork from Schurrle to cut inside and get a shooting chance. He's quickly closed down though and the hosts try again. This time it's Ozil down the right and it's another fine stop from form as Khedira looks for the corner. He then makes way for Max Kruse.
83 minOFF THE BAR! Oh my word what an effort from Boateng! A corner comes out to him and he takes a couple of touches before rifling a magnificent strike against the bar from 30 yards.
85 minGERMANY SUB: Schurrle makes way for Mario Gotze. Not a half bad sub to have for Germany! Ireland cannot turn off just yet.
87 minCLOSE! So, so close from Gotze. He picks up the ball just inside the box and rolle across goal with his right foot but it goes a matter of centimetres wide of the goal.
88 minGERMANY SUB: Muller has had a great game and he now makes way for Leverkusen's Sidney Sam. An injection of sheer pace in the last few minutes.
90+1 minGOAL! Germany 3-0 Ireland (Mesut Ozil)
90+1 minThat is a lovely goal. Germany break from an Ireland corner. Sam finds Kroos inside and he plays through Ozil who finishes with the deftest of touches over the keeper.
90+3 minFULL-TIME: Germany 3-0 Ireland
9.37pmGERMANY QUALIFY FOR WORLD CUP
9.38pmSo Germany top the group as expected and that was another thoroughly professional performance. There were a few weaknesses at the back that stronger sides might exploit, but they will be one of the big favourites for the tournament.
9.39pmThanks for joining me for this one. That's all from me, but do check on site for the analysis that will be up in roughly half an hour. Goodbye!