Yorkshire, who were in the title hunt until the final day last season, got off to a flying start to the new campaign after Gerard Brophy’s unbeaten 177 had undermined the home side’s confidence.
Batting again after falling 82 behind in the first innings, the newly-promoted county crumbled to be all out for 137 in 38.5 overs, leaving plenty of time for the visitors to clear off the 56 runs for a thumping victory.
Adam Lyth reached an unbeaten 29 when he hit the winning boundary through extra cover after putting on 40 with Championship debutant Joe Root (21 not out).
Rashid followed up his six-wicket return in the first innings by taking five for 37 to post overall figures of 11 for 114 as Worcestershire revealed many of the frailties which wrecked previous attempts to establish a foothold at the top level.
The 23-year-old England Lions leg-spinner was hit for two sixes while conceding 27 runs in his first three overs, but skipper Andrew Gale kept faith with a potential match-winner and reaped the rewards when Rashid took five for 10 in the space of 40 deliveries.
Yorkshire’s seamers made the early inroads by removing the top-three batsmen before Worcestershire could wipe out their deficit.
Daryl Mitchell (30) fell lbw to Steven Patterson and Ryan Sidebottom, having made a career-best 61 with the bat, accounted for James Cameron and Vikram Solanki.
A thin edge on the leg-side cost Solanki his wicket and set the pattern for the collapse that followed as Rashid preyed on the batsmen with control and flight as well as some turn on a dry surface.
Moeen Ali (21) paddled a catch to Lyth, running around from slip, and from that point Worcestershire lost seven for 35 in 11 overs.
Patterson also played a key role by moving one away to have danger man Alexei Kervezee caught behind for 52, a dismissal that opened the door for Rashid to spin through the lower order with minimal resistance.
While Yorkshire can reasonably look forward to chasing top spot again, Worcestershire are already looking at a familiar script.
Relegated in each of three previous seasons in Division One, they have won only one of their past 38 top-flight matches.
Yet this game was going well for them until Brophy and Sidebottom turned the tide in an eighth-wicket stand which yielded 149 before they were parted after batting together for 55 overs.
Sidebottom played around a straight ball from Matt Mason, but Brophy continued his serene progress, with 27 fours and a six in his highest innings since 2004 when he made 181 for Northamptonshire against Sussex.
For Chris Waters’s analysis and report, read Sports Monday inside your Yorkshire Post.