Rodriguez’s second-half double made it back-to-back victories over European opposition with a week to go until the start of the Premier League season.
Italian top-flight outfit Parma made this a more difficult test than the 6-1 mid-week win over Nice.
But the Clarets still had enough about them to turn up the power and chalk up a morale-boosting success secured by two headers from the returning Rodriguez.
The summer signing followed his first goal back at Turf Moor again Nice with two more predatory efforts in front of the Jimmy McIlroy Stand.
And like a number of his team-mates, he must now wait to see whether he will face former club Southampton when the real thing starts at Turf Moor next Saturday.
Dyche had suggested his final pre-season starting line-up would not necessarily reflect that which sets out against the Saints for a second season running.
And it certainly appeared the manager was using the last chance to spread some game-time across his squad as just four players who started the rout against Nice were in from the off here.
Nick Pope returned in goal – wearing the number one jersey – after missing the last three warm-up fixtures with a slight groin problem.
And Ben Gibson and Robbie Brady were also back after similar absences.
Unfortunately, Brady’s comeback lasted little more than half an hour as the wingman succumbed to what seemed to be a repeat of the rib injury that had limited his movement.
Jack Cork didn’t make it to half-time either as he picked up a knock in what was a far more competitive affair than the romp against Nice.
Parma’s Serie A season doesn’t start until a fortnight after the Premier League but the ‘Crusaders’ certainly didn’t look under-cooked on a stiflingly warm and muggy afternoon.
That meant a decent wok-out for Pope, as he looks to reclaim a starting slot following Tom Heaton’s departure to Aston Villa.
And the England man was certainly the busier of the two goalkeepers before the break, grabbing a mis-cued effort from Yann Karamoh early on when the on-loan Inter Milan forward should have scored and then saving well at the feet of Juraj Kucka.
The lively Roberto Inglese was also a threat for the Italians and went closest to breaking the deadlock with a flicked header from a corner which hit the underside of the bar.
Burnley found openings harder to come by, although a moment of magic from Chris Wood almost gave them a half-time lead.
Pope was involved again with a piece of smart footwork in a one-two with Matt Lowton, who then delivered a long ball over the Parma defence for Wood to meet with a first-time volley he steered just over the top.
Wood was then given a breather at half time as Ashley Barnes came on to partner Rodriguez.
And after Inglese had again tested Pope with a fizzing long-range effort, it was Rodriguez who came alive to put the Clarets in control with a quick-fire double strike.
The summer signing followed up his mid-week strike seven minutes into the second half when he stooped to nod in a deflected cross from Aaron Lennon.
And four minutes later he was on target again with a more astute finish, timing his run perfectly to meet a deep Lowton cross with a header back across goal and into the far corner of the net.
Reflecting their match readiness, the Clarets finished the stronger as Dyche introduced a handful of substitutes to reflect the options he has at his disposal.
And while there were no further goals – Barnes coming closest following a neat link-up with lively substitute Nahki Wells – Pope and his re-shaped back four saw out the clean sheet to underline the belief Dyche’s men are ready to hit the ground running in a week’s time.
Burnley: Pope; Lowton (Bardsley 73), Gibson (Dunne 67), Mee, Taylor (Pieters 67); Lennon (Gudmundsson 67), Hendrick (Benson 73), Cork (Westwood 38), Brady (McNeil 32); Rodriguez (Wells 73), Wood (Barnes HT). Hart, Legzdins, Vydra.
Parma: Sepe; Laurini, Dermaku, Alves, Gagliolo; Kucka, Brugman, Barilla; Kulusevski, Karamoh; Inglese. Substitutes used: Iacoponi, Cornelius, Sprocati, Gazzola, Machin, Ceravolo, Minari.
Referee: Paul Tierney
Attendance: 4,846 (Parma 52)