Dhananjaya made 93, his best ODI score, to help Sri Lanka recover from 96 for six to make 213.
And Theekshana then took three wickets in the space of two overs to derail the Dutch chase in a 21-run victory.
In the other game of the day in Harare, Ireland eased to victory in the 7th place play-off semi-final, beating the USA by six wickets.
Sri Lanka pushed to the limit by the Netherlands
The Netherlands signalled their intent from the very first ball of their clash with Sri Lanka, with Pathum Nissanka sent on his way for a duck by Logan van Beek.
That was part of a dream start for the Dutch, who quickly had the Sri Lankans 34 for four as Van Beek (3/26) showed his skill with the ball four days on from his heroics with the bat against the West Indies.
It required a sensational knock from Dhananjaya de Silva to get Sri Lanka to 213 all out, and even that did not look like it would be anywhere near enough.
However, just as the Netherlands seemed to be on track in reply, Maheesh Theekshana (3/31) swung the momentum with three quick wickets as the Netherlands eventually fell 21 runs short.
They had started so well. Nissanka departed after just one ball, before Ryan Klein had Kusal Mendis (10) trapped in front in the fourth over.
Van Beek added Sadeera Samarawickrama (1) and Charith Asalanka (2), bringing Dhananjaya to the crease.
He began to rebuild with Dimuth Karunaratne, who then fell for 33, with skipper Dasun Shanaka then departing for five, Saqib Zulfiqar (2/48) accounting for both men.
Wanindu Hasaranga provided some useful runs, making 20 in a 35-run stand with Dhananjaya. And after he fell LBW to Bas de Leede (3/42), Theekshana joined Dhananjaya.
The duo added 77 runs, taking Sri Lanka past 200 before both getting out in the space of three deliveries.
A target of 214 was certainly in reach for the Dutch, albeit on a tricky wicket for the batters.
Their cause was not helped by both openers falling for ducks, Lahiru Kumara removing Vikramjit Singh and Dilshan Madushanka accounting for Max O’Dowd.
However a 77-run partnership between Wesley Barresi (52) and De Leede (41) got the chase back on track. It was ended by some sharp work in the field by Shanaka, with Barresi short of his ground while trying to steal a single.
Teja Nidamanuru then became the third Dutch batter to go for a duck, bowled by Hasaranga. In came Scott Edwards and the skipper quickly settled in alongside De Leede, the pair adding 36 in six overs.
Sri Lanka were in desperate need of a breakthrough and it came from Theekshana, who snuck one through the defences of De Leede.
He added two more in his next over, including the vital wicket of Van Beek, before another run-out saw Shariz Ahmed depart for two, leaving the Netherlands on 151 for eight.
Edwards and Ryan Klein added 25, inching closer with the required rate not an issue, but a perfect wrong’un from Hasaranga was too good for Klein (5).
That left the final pair with 38 to get in 17 overs and the in-form Edwards helped get them close, but the skipper was left stranded unbeaten on 67 when Aryan Dutt was clean bowled by Shanaka.
Ireland make it two in a row
Ireland backed up their win over the UAE in their final Group B match by seeing off the USA by six wickets in Harare in the 7th place play-off semi-final.
Craig Young was the pick of the bowlers for Ireland, as they bowled out their opponents for just 196 having elected to field first at the Takashinga Cricket Club.
Steven Taylor (23) and Sushant Modani had put on 33 for the first wicket when Young struck twice in as many balls, Taylor caught by Gareth Delany before skipper Monank Patel was bowled first ball.
That brought Saiteja Mukkamalla to the crease, with he and Modani adding 88 runs for the third wicket before Mukkamalla was run out for 55.
Andy McBrine then removed Gajanand Singh caught and bowled for ten, with Abhishek Paradkar caught behind off Barry McCarthy for a duck.
Lorcan Tucker added another dismissal straight afterwards as the USA started to stumble, catching Modani for 55 off the bowling of McBrine.
Young (3/35) returned to take Nisarg Patel and the USA were suddenly 155 for seven and scrambling.
Usman Rafiq provided some late impetus, with an unbeaten 28, but the wickets kept falling around him, Ali Khan the last to go as the USA were bowled out in the 43rd over.
Needing 197 to win, Ireland got off to a flying start, Paul Stirling hitting a 45-ball 58 to lay the foundations. He was pinned in front by Nosthush Kenjige (2/41), with opening partner McBrine (35) the next to fall.
Skipper Andy Balbirnie (45 not out) made sure there were no nerves however, adding 38 with Harry Tector (25) and 29 with Tucker (25) to take Ireland to the brink before Curtis Campher joined him to see the side home with 15.4 overs to spare.
Windies look for a miracle against Scotland
Successive defeats to Zimbabwe and the Netherlands have left the West Indies with a mountain to climb to finish in the top two of the Super Six, and their challenge begins against Scotland.
Shai Hope’s side are already in must-win territory, but can keep the pressure on with a victory, against a Scotland team who already have two points under their belts.
Richie Berrington and his team won their first three matches before coming unstuck against Sri Lanka, but could boost their World Cup qualification hopes with a win in Harare.
Scores in brief
Netherlands v Sri Lanka at Queens Sports Club, Bulawayo by ten wickets
Sri Lanka 213 all out in 47.4 overs (Dhananjaya de Silva 93, Dimuth Karunaratne 33; Logan van Beek 3/26, Bas de Leede 3/42)
Netherlands 192 in 40 overs (Scott Edwards 67 not out, Wesley Barresi 52; Maheesh Theekshana 3/31, Wanindu Hasaranga 2/53)
Ireland beat USA at Takashinga Cricket Club, Harare by six wickets
USA 196 all out in 42.4 overs (Sushant Modani 55, Saiteja Mukkamalla 55; Craig Young 3/35, Andy McBrine 2/19)
Ireland 197/4 in 34.2 overs (Paul Stirling 58, Andy Balbirnie 45*; Nosthush Kenjige 2/41, Nisarg Patel 1/20)
Saturday 1 July – Fixtures
Super Six
Scotland v West Indies at Harare Sports Club, Harare