Both players had seen their schedule impacted by rain earlier in the tournament, leaving them with a tough test at the Lindner Family Tennis Center.

Djokovic completed his rain delayed match against Bulgaria’s Grigor Dimitrov as the Serbian star overcame the defending champion 2-6, 6-3, 6-4 after the match resumed in the third set.

The Wimbledon champion had only a short recovery before facing Canada’s Milos Raonic in the quarter-finals.

Djokovic battled through a tough match against the Canadian to emerge as an 7-5, 4-6, 6-3 winner.

The Serbian is now just two victories away from winning the only Association of Tennis Professionals Masters 1000 event he has yet to win.

He will now face the challenge of Croatia’s Marin Cilic, who completed a 7-6, 3-6, 6-4 win over Russia’s Karen Khachanov before beating Spain’s Pablo Carreno-Busta 7-6, 6-4 in the quarter-finals.

Switzerland’s Roger Federer and Belgium’s David Goffin also ended the day with two victories to set up a semi-final meeting.

Goffin beat South Africa’s Wimbledon runner-up Kevin Anderson 6-2, 6-4 before winning 7-6, 7-6 against Argentina’s Juan Martin Del Potro.

Federer was a 6-1, 7-6 winner against Argentina’s Leonardo Mayer before he clinched a 6-7, 7-6, 6-2 win over fellow Swiss Stan Wawrinka.

In the women’s tournament, Romania’s Halep began the day by winning 7-5, 6-4 against Australia’s Ashleigh Barty.

She finished by overcoming Ukraine’s Lesia Tsurenko 6-4, 6-1 to seal her semi-final spot.

The world number one will now face Belarus’ Aryna Sabalenka, who beat the Madison Keys of the United States 6-3, 6-4 in her quarter-final match.

Czech Republic’s Petra Kvitova was a 7-5, 5-7, 6-3 winner against Belgium’s Elise Mertens to reach the last four.

She will now play Kiki Bertens after the Dutch player beat Ukraine’s Elina Svitolina 6-4, 6-3 at the Women's Tennis Association Premier 5 category event.