Cyle Larin's first half goal was disallowed by the referee as the Besiktas forward fouled his opponent before his header.
However, Besiktas broke the deadlock in the minute of 61 as the visitors' Croatian defender Domagoj Vida scored with a header. Algerian winger Rachid Ghezzal assisted Vida.
Besiktas secured the narrow win in the week 14 to rise in standings, boosting their points to 25, to be placed fourth.
They joined the title race against archrivals Galatasaray and Fenerbahce, as well as the league leaders Aytemiz Alanyaspor.
Galatasaray and Fenerbahce had 26 points each.
Alanyaspor racked up 27 points to top Super Lig standings.
The losing team, Ankaragucu had 9 points to be in the 20th spot.
Vida carries on scoring
Black Eagles regular Vida scored two Super Lig goals this season.
He previously scored a classy goal against Buyuksehir Belediye Erzurumspor last week that Besiktas won 4-0 at home Vodafone Park.
Week 14 results:
Atakas Hatayspor - Trabzonspor: 0-1
Galatasaray - Goztepe: 3-1
Buyuksehir Belediye Erzurumspor - Yukatel Denizlispor: 1-2
Aytemiz Alanyaspor - Yeni Malatyaspor: 1-1
Kasimpasa - Gaziantep FK: 0-4
Fenerbahce - Medipol Basaksehir: 4-1
Demir Grup Sivasspor - Genclerbirligi: 3-1
Hes Kablo Kayserispor - İttifak Holding Konyaspor: 1-2
MKE Ankaragucu - Besiktas: 0-1
Çaykur Rizespor - Fraport TAV Antalyaspor: 2-1
League table:
| Clubs | P | W | D | L | GF | GA | +/- | Pts |
| 1.AYTEMIZ ALANYASPOR | 14 | 8 | 3 | 3 | 23 | 9 | 14 | 27 |
| 2.GALATASARAY | 13 | 8 | 2 | 3 | 23 | 10 | 13 | 26 |
| 3.FENERBAHCE | 14 | 8 | 2 | 4 | 27 | 20 | 7 | 26 |
| 4.BESIKTAS | 13 | 8 | 1 | 4 | 26 | 19 | 7 | 25 |
| 5.GAZIANTEP FK | 13 | 6 | 6 | 1 | 24 | 15 | 9 | 24 |
| 6.ATAKAS HATAYSPOR | 13 | 6 | 3 | 4 | 14 | 16 | -2 | 21 |
| 7.FATIH KARAGUMRUK | 13 | 5 | 5 | 3 | 22 | 16 | 6 | 20 |
| 8.YENI MALATYASPOR | 13 | 5 | 5 | 3 | 17 | 14 | 3 | 20 |
| 9.TRABZONSPOR | 14 | 5 | 5 | 4 | 16 | 17 | -1 | 20 |
| 10.ITTIFAK HOLDING KONYASPOR | 13 | 5 | 3 | 5 | 17 | 13 | 4 | 18 |
| 11.GOZTEPE | 14 | 4 | 6 | 4 | 20 | 17 | 3 | 18 |
| 12.CAYKUR RIZESPOR | 13 | 5 | 3 | 5 | 19 | 21 | -2 | 18 |
| 13.KASIMPASA | 14 | 5 | 3 | 6 | 16 | 21 | -5 | 18 |
| 14.DEMIR GRUP SIVASSPOR | 13 | 4 | 5 | 4 | 13 | 13 | 0 | 17 |
| 15.FRAPORT-TAV ANTALYASPOR | 14 | 4 | 5 | 5 | 15 | 18 | -3 | 17 |
| 16.MEDIPOL BASAKSEHIR | 13 | 4 | 3 | 6 | 19 | 22 | -3 | 15 |
| 17.YUKATEL DENIZLISPOR | 13 | 3 | 3 | 7 | 13 | 22 | -9 | 12 |
| 18.GENCLERBIRLIGI | 13 | 3 | 3 | 7 | 11 | 21 | -10 | 12 |
| 19.HES KABLO KAYSERISPOR | 13 | 2 | 4 | 7 | 7 | 16 | -9 | 10 |
| 20.MKE ANKARAGUCU | 13 | 2 | 3 | 8 | 14 | 21 | -7 | 9 |
| 21.BUYUKSEHIR BELEDIYE ERZURUMSPOR | 14 | 2 | 3 | 9 | 12 | 27 | -15 | 9 |
