He missed a penalty in a frustrating first half for the hosts, however Hamburg’s Bobby Wood saw red after elbowing Dominique Heintz.
The floodgates then opened as Modeste redeemed himself for his earlier miss, although his first goal could yet be credited to Simon Zoller.
Köln go back up to fourth in table, whilst Hamburg remain rooted to the bottom, and in all sorts of trouble.
Three changes each from Pokal victories
Köln have started the season in impressive fashion but lost for the first time last weekend against Hertha BSC. However in midweek they beat TSG 1899 Hoffenheim in the DFB-Pokal 2-1 in extra time.
Peter Stöger was able to start Dominic Maroh following his recovery from a rib injury, with Pawel Olkowski dropping to the bench, although an early collision with Wood meant his comeback was brief. There were two other changes from midweek, as Marco Höger replaced Konstantin Rausch and Yuya Osaka returning at the expense of Zoller.
Hamburg are without a win in the league but beat third-tier Hallescher FC in the Pokal on Tuesday, with Markus Gisdol keeping faith in most of the team that started that game, with both Wood and Pierre-Michel Lasogga starting up front together again.
Ashton Götz replaced the suspended Dennis Diekmeier after his sending off in the abject display against Eintracht Frankfurt nine days earlier, Johan Djourou returned from a hamstring injury and Lewis Holtby was restored from the bench. Albin Ekdal and Cléber Reis dropped out.
Modeste misses chance to give Köln the lead
Köln had a very credible shout for a penalty in the early minutes, when Gideon Jung clearly bounced the ball onto the ground, however the referee wasn’t interested despite Modeste’s protests.
The hosts were the form side, but it wasn’t really showing. Wood should have done better with a cross from Douglas Santos, but his poor first touch still needed sending wide by Timo Horn.
Modeste cut a frustrated figure in the first half. He had a header deflected wide after Frederick Sörensen found him with a deep cross. He was then harshly booked for handball in the Hamburg box, despite it being only the slightest of undeliberate touches at best. After the Jung decision, it did not adhere referee Benjamin Brand to the home supporters.
Both sides had further half chances to score, with Artjoms Rudnevs hitting the side netting and Osako having a chance blocked by Götz, and at the other end a promising Hamburg attack broke down when Filip Kostic crossed straight to a Köln shirt in the box.
Frustration amongst the fans at the referee was growing, with Höger and former Hamburg man Rudnevs going in the book, but then Brand awarded them a penalty, when Osako was bundled to the ground by Götz. Modeste has been in superb form this season, but surprisingly the Bundesliga’s top scorer could only hit the post from the spot.
Wood stupidity punished by sublime Modeste
Little of note happened in the early stages of the second half, but the game changed when Wood got himself foolishly sent off. As Hamburg took a free-kick up the pitch, he hustled with Heintz, before elbowing him in the stomach, seemingly unprovoked. Brand didn’t see it, but his assistant did, and the American forward was subsequently shown a red card.
Minutes later and Modeste appeared to finally rediscover his scoring form. An excellent cross from Zoller found the striker, who may have got the slightest of touches on it as it went in, although there will be debate over whether it was actually Zoller’s goal. He certainly gave him some credit in the celebrations that followed.
Köln were now on top, although further chances went astray. Matthias Lehmann’s attempt was almost put into his own net by Johan Djourou, whose blushes were spared by René Adler, then Modeste mishit a chance after a great ball from Osako, before Zoller put a chance of his own wide.
But Modeste went on to put the game beyond Hamburg. He struck in the second from a Marcel Risse cross, and the two combined again minutes later. Risse this time played him through the middle, and Modeste completed his hat-trick through the legs of Adler.
Köln return to the top four as a result, but the misery goes on for Hamburg. Without a win in the league all season, just two goals, and at over 600 minutes they are on their longest-ever Bundesliga goal drought. And they play Borussia Dortmund next.