The 32-year-old all-rounder, who is the Yorkshire beneficiary for 2015, scored 84 against the Leeds-Bradford students, an innings that contained 62 runs in boundaries, many of them punched delightfully through mid-on.
In partnership with Andrew Hodd, who made 54 and also played some delightful straight drives, Pyrah helped Yorkshire to 329-9 declared after they were sent into bat, the pair adding 116 for the sixth wicket from 113 balls.
They lifted Yorkshire from a slightly wobbly 148-5 by virtue of controlled and aggressive strokeplay against a side who stuck to their task admirably, and who closed the day on 46-0.
Of course, the champions are not quite at champion strength for this game – nor, indeed, for their opening three County Championship matches – due to six players being on England’s tour to the West Indies.
That would the test the resources of any side but it does, of course, afford opportunities for other players – among them Pyrah and Hodd.
Their efforts yesterday showed Yorkshire’s strength in depth, a strength that gives rise to the belief that they can cope with the loss of their England contingent.
Pyrah and Hodd will play in the opening Championship game against Worcestershire at New Road on Sunday, where Hodd will take the gloves in the absence of England’s Jonny Bairstow.
Hodd is unlikely to open the batting, however, having initially been earmarked as a candidate to deputise for Adam Lyth.
That duty seems set to rest with Will Rhodes, the 20-year-old all-rounder who opened here with Alex Lees after impressing on his first-class debut last month against MCC.
Before a small but decent-sized crowd given the nature of the fixture, Rhodes was frustrated yesterday when he fell in the fourth over, brilliantly caught down the leg-side by wicketkeeper Chris Wakefield off Liam Watkinson for a single.
Yorkshire, who omitted pace bowler Matthew Fisher from their 12 and who will welcome new overseas signing Cheteshwar Pujara to Headingley tomorrow, steadied the ship through a patient second-wicket stand between Lees and Dan Hodgson.
Hodgson, the 25-year-old right-hander, is another hoping to take his chance with the England players away, and he looked in good touch on his way to 35.
The stand had realised 72 when Hodgson was bowled by Harry Rouse, pushing forward, and Yorkshire lost their third wicket when captain Andrew Gale went leg-before to Doug Pratt.
There was just time for Lees to reach his fifty before lunch, made from 89 balls with seven fours.
Jack Leaning fell shortly after the break, bowled by former Yorkshire pace bowler Alex Lilley, who tried to employ a fuller length on a pitch where the ball had a tendency to sit up a touch.
When Lees was caught behind off Pratt for 63, made from 125 deliveries with seven fours, Yorkshire were in danger of falling short of the type of total they would have expected to make.
But Pyrah and Hodd joined forces and batted with what the coaches like to call “positive intent”.
In no time, or so it seemed, Pyrah had fifty to his name from 63 balls, Hodd reaching the same landmark from 55 deliveries.
Both players made the on-drive – one of the hardest shots in the game – look like child’s play at times, plundering 51 runs in one three-over period in which Leeds-Bradford, temporarily, lost their bearings.
It needed the impressive Lilley to get rid of both men, the 22-year-old left-armer – who played one first-class game for Yorkshire in 2011 – pinning them lbw.
Hodd went first, followed by Pyrah in the last over before tea, with Tim Bresnan slapping a delivery from the left-arm spinner Joe Ellis-Grewal to cover after the break and Steve Patterson losing his stumps to Lilley.
Patterson played a terrific little innings of 41, made from 52 balls with seven fours, including a majestic back foot cover drive off Rouse in the direction of the East Stand of which Pujara would surely be proud.
After Yorkshire declared, leaving themselves an hour at their opponents, Steve Bullen and Henry Thompson each fought through to finish unbeaten on 21.