Dutch pair book slot in last eight.
Griekspoor and Van der Duim advanced following a clinical 6-1, 6-1 victory over young Bahraini wildcards Khaled Al Mosawi and Yousef Qaed.
Ranked 1,200th in the world, the third seeds now meet the pairing of Andre Gaspar Murta of Portugal and Ashwin Vijayragavan of India in the last eight.
Murta and Vijayragavan were also victorious yesterday in their first round encounter against Bahrain's Khaled Al Thawadi and Kuwait's Mohammed Reda. The 1,686th ranked duo ousted their Gulf rivals 6-0, 6-2.
Both matches were part of the action-packed order-of-play in yesterday's opening day of the International Tennis Federation (ITF) Men's Pro Circuit tournament.
This year's event is being held under the patronage of Supreme Council for Youth and Sports chairman and Bahrain Olympic Committee president Shaikh Nasser bin Hamad Al Khalifa, and it is being sponsored by Gulf Petrochemical Industries Company, Al Salam Bank and Bahrain Duty Free.
Also advancing to the quarter-finals last night were German fourth seeds Peter Heller and Dominik Schulz, together ranked 1,348th in the world. They overcame a tough challenge from Belgian tandem Joris de Loore and Jeroen Vanneste (ranked 1,408th) 7-5, 6-3 to book their seats in the round of eight.
They will now face the Indian-Sri Lankan partnership of Sagar Manjanna and Dineshkanthan Thangarajah, who were made to sweat in it out before beating Delf Gohlke and Christian Hirschmueller of Germany 6-4, 7-5.
Frenchmen Maxime Chazal and Romain Sichez (ranked 2,224th) had a more comfortable outing in their 6-1, 6-1 win over Bahraini wildcards Hassan Abdulnabi and Abdulrahman Janahi.
Indians Kunal Anand and Ronak Manuja (ranked 2,725th) had a tougher time, needing to battle back from a set down and force a super tie-break in defeating Zimbabwe-Russia alliance Tinotenda Chanakira and Egor Kovalev 3-6, 6-4, 11-9.
Chazal and Sichez now take on men's doubles seconds seeds Riccardo Maiga of Switzerland and Ruan Roelofse of South Africa, who are ranked 940th in the world. Anand and Manuja face off with top seeds Christian Rodriguez of Colombia and Jordi Samper-Montana of Spain, who are 874th.
Meanwhile, also yesterday, Schulz had double the reason to celebrate, making it through to the second round of the men's singles competition.
The eighth seed, ranked 777th individually, ousted fellow-German Hirschmueller (945th) 6-2, 6-4.
Belgian De Loore, who lost his doubles clash, made up for it in the singles where he is seeded fifth. The 550th-ranked player in the world beat Lukas Koncilia of Austria (1,132nd) 7-6 (3), 6-1 to secure his place in the second round.
De Loore's doubles partner Vanneste (825th) also had success in his singles match, beating Germany's Nico Matic (829th) 6-4, 3-6, 6-2.
Yesterday's last player to march through was Dutchman Lennert Van der Linden (943rd), who beat Hicham Khaddari of Morocco (949th) 6-2, 6-3.
Action in the championship continues today with 12 men's singles matches, starting at 10am and then resuming at 3.30pm following a midday break. All are welcome to watch the games. Entrance to BTC is free of charge.
(All Men's Singles matches)
Starting at 10.30am: Egor Kovalev (RUS) vs Kevin Jordi (SUI); 4-Ruan Roelofse (RSA) vs Vaja Uzakov (UZB); Denis Gremelmayr (GER) vs Delf Gohlke (GER); Romain Sichez (FRA) vs Kunal Anand (IND)
Starting not before 3.30pm: 1-Jordi Samper-Montana (ESP) vs Abdulrahman Janahi (BRN); Maxime Chazal (FRA) vs Sagar Manjanna (IND); Khaled Al Mosawi (BRN) vs 7-Kevin Griekspoor (NED); 3-Antal Van der Duim (NED) vs Riccardo Maiga (SUI)
Starting not before 5pm: Alborz Akhavan (GER) vs Yousef Qaed (BRN); Ronak Manuja (IND) vs Mohammed Reda (KUW); 2-Peter Heller (GER) vs Ashwin Vijayragavan (IND); 6-Christian Rodriguez (COL) vs Andre Gaspar Murta (POR).
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