Marcus Bald saved a stoppage time penalty as Valley secured a point at Boldmere St Michaels.
Bald's dramatic late double save ensured a halt to a run of three successive defeats for Rugby after a marked improvement in performance.
Town boss Grant Joshua rang the changes sixteen days on from their last outing - a disappointing 1-0 defeat at Shepshed, with recalls to the starting line-up for Rivel Mardenborough, Teddy Rowe and Cairo Taylor.
There was also a debut up-front for new signing Kobi Bivens, with Bleu McNeil and Sam Tye dropping down to the bench, Stan Anaebonam unavailable and Tyrell Hamilton having departed the club.
It was generally an uneventful first half, although Rowe and Boldmere's Jack Burgess did both send in dangerous crosses early on - which Bald and his opposite number Jon Brown both doing well to deal with them.
A Geoffrey Lundoloki long-ranger was also comfortably dealt with by Brown, whilst Bald smothered Kye Bilton's low strike across the box, before the best chance of the opening forty-five saw Bivens just unable to connect to a neat cross from Taylor after Rowe had fed him on the right-hand side.
Shortly before the interval, James Tague saw his shot from the edge of the Rugby box blocked by Josh Thomas and then he lifted the loose ball way over.
Town started the new period in purposeful manner though, with Mardenborough soon putting a close range effort straight at Brown.
Brown then pulled off an excellent fingertip save to push Bivens's header over the bar after Nathan Kabeya had cut in from the right and picked out the Valley newbie with a nicely flighted-delivery.
However, the hosts responded well to Town's increased dynamism and stepped up a gear themselves too. Tague's free-kick from a dangerous position on the edge of the box was caught by Bald, after the Rugby keeper had originally been punished for bringing down Harry Crook from Burgess's headed flick-on.
Caine Elliott did well to block a further on-target strike, with another Tague free-kick from a wider angle sailing harmlessly high and wide of the frame.
Crook then released Mikes' sub Tolani Omotola with a pass in behind the Town defence, with Bald well-positioned to gather Omotola's final lifted shot. As the game entered its final ten minutes, it opened up further, and both sides looked for a winner.
Griffin's searching ball down the left channel found Sam Tye in some space, and the Valley sub skipped around Brown before guiding the ball across the face of the goal from a tight angle.
Unfortunately, there was no Rugby player on hand to finish it off, and from the resulting clearance Jack Concannon was crowded out on the edge of the box.
A further weak effort from Tye was saved by Brown, with the Boldmere keeper then pushing away Trey Charles's well-struck effort from more than twenty yards.
Another Boldmere free-kick from a dangerous position - this time from Burgess - flew way over the bar, before referee Ryan Price looked to have intervened with the defining moment in the game when he harshly decided that Thomas had fouled Ben Lund near the by-line after the pair had become entangled.
However, Bald was down quickly to keep out Danny O'Callaghan's low spot-kick, before doing equally as well to keep out a follow-up effort, leading to a brief goalmouth scramble and then O'Callaghan finally acrobatically lifting one over the target to ensure that Town completed their first goal-less draw of the season so far.
After the final whistle there was something of a confrontation between the two sets of players which resulted in red cards for Boldmere's Pedro Lima and Valley's Bleu McNeil.
Valley
Line-up: Bald; Kabeya, Lundoloki, Thomas, Harris; Elliott, Griffin (McNeil 89'), Rowe (Concannon 72'); Taylor (Charles 72'), Mardenborough, Bivens (Tye 82'). Subs not used: Dulgheru. Booked: Griffin, Bald, Lundoloki, Thomas. Sent off: McNeil (after FT).
