The first half proved to be something of a non-event with Diamonds unable to find any rhythm while Rugby remained resolute.
Nic Evangelinos fired over early on but the closest Diamonds came was when Mason Rowley almost put through his own net from a Nabil Shariff cross.
Rugby went close when Chris Sterling’s shot was deflected over the bar and Diamonds were also hit by the loss of Jack Ashton to injury before the break.
Tom Lorraine went bundled an effort wide as Diamonds started the second half on the front foot but Lorraine soon found himself partnering Brad Harris at centre-half after Liam Dolman was also forced off with an injury.
And Diamonds paid the price when they fell behind on 58 minutes. Daniel Campbell crossed from the left and Sterling’s near-post header looped up and over Ben Heath and dropped into the net.
But Diamonds responded quickly and they drew level six minutes later when a ball was only half-cleared and Evangelinos hammered it into the top corner.
Campbell flicked a header just wide for Rugby and Heath produced a fine save to tip away a Kyle Rowley piledriver from fully 30 yards.
Diamonds came on strong towards the end but they were unable to find a winner with Shariff seeing a late effort deflected agonisingly wide.
Kettering Town beat United Counties League Premier Division leaders Peterborough Sports 4-2 in a penalty shoot-out after a 3-3 draw to move into the semi-finals of the NFA Hillier Senior Cup.
Former Kettering man Avelino Vieira gave the visitors the lead inside the first minute.
Brett Solkhon levelled things up soon after but Vieira struck again to regain the lead for the visitors.
However, it was all-square before half-time as Matthew Barnes-Homer grabbed his first goal for the Poppies.
Kettering took the lead for the first time with 16 minutes to go through substitute Jordan Wilson but Vieira completed his hat-trick to level things up late on.
But the Poppies won the resulting shoot-out with Solkhon converting the winning penalty.
Corby Town also won on penalties as they edged out Cogenhoe 4-3 on spot-kicks after a 2-2 draw.
Cogenhoe took the lead just past the half-hour mark but the Steelmen drew level through new signing Phil Trainer on 37 minutes.
Corby took the lead just past the hour when Gary Mills’ other new arrival, Stefan Moore opened his account for the club from the penalty spot.
Desborough Town also booked their place in the last four as they saw off UCL Premier Division rivals Sileby Rangers 4-1 at the Waterworks Field.
However, Wellingborough Town’s hopes were ended in a 5-1 defeat at Vanarama National League North side Brackley Town.