Randhawa and paceman Ben Sanderson, another former Yorkshire man, both impressed with the ball in the three-day Unicorns Championship match at Shifnal.
But Shropshire once again found runs in short supply as they pulled up considerably short of their daunting second innings victory target of 374.
It means Shropshire have lost both of their Championship matches this season with the next clash at home to Oxfordshire at Bridgnorth between July 6-8.
Herefordshire opted to bat first on what appeared to be a good looking pitch but found runs hard to come by on the opening day as they were removed for 152.
Randhawa, a former England under-19 international, claimed 4-21, with his efforts well backed up by opening bowler Sanderson (3-17) and debutant Ross Aucott (3-36).
Wolverhampton’s Aucott was one of three new boys in the Shropshire side along with Oswestry’s Joe Carrasco and Quatt’s Adrian Evans.
Carrasco (29) and Randhawa (24) initially laid solid foundations to the Shropshire reply by putting on 50 for the first wicket.
Wickets then started to tumble and, despite a defiant 55 from the experienced James Ralph, the county were dismissed for 143, much of the damage inflicted by left-arm spinner Brad Wadlan who claimed 6-26.
Herefordshire were more impressive with the bat second time out, eventually declaring on 364-8 to establish a 373 run lead.
Former Glamorgan batsman Michael O’Shea top scored with 70 while there were also half centuries for Wadlan (67), Joe Dodd (63no) and Dave Ball (53).
Randhawa plugged away to bowl 43 overs for 5-146 and Sanderson picked up three more wickets in a spell worth 3-49.
Shropshire started the final day needing 306 for victory but, having been 67-1 overnight, they disappointingly fell away to be dismissed for 113 with the match all over a little after noon.
Carrasco top scored with 47 and fellow newcomer Evans made 23 but Shropshire’s fate was sealed when they lost their final five wickets in quick succession for the addition of just one run.
Shropshire’s chairman of selectors Brian Foxall said: “We always knew the final target of 374 to win was going to be tough.
“We needed to bat well for an hour at the start of the final morning but instead we quickly lost wickets and were really up against it.
“It was a disappointing result but there were some positives, notably the bowling efforts of Gurman Randhawa and Ben Sanderson who both performed heroically while Joe Carrasco batted well on his debut.”