Warwickshire 315 (Rhodes 102, Briggs 99, Murtagh 6-83) and 58 for 2 beat Middlesex 121 (Hannon-Dalby 5-29) and 251 (Robson 107*, Higgins 57) by eight wickets
Sam Robson's tenacious, unbeaten hundred proved to be in vain for Middlesex as they slid into the LV= Insurance County Championship relegation places after defeat to Warwickshire at Lord's.
Warwickshire's bowlers stuck to their task, dismissing Middlesex for 251 in their second innings despite a spirited knock of almost seven hours by Robson, who carried his bat for 107 not out.
Ryan Higgins provided support with 57, but Craig Miles' 3 for 52 was backed up by Olly Hannon-Dalby, who also took three wickets to finish with match figures of 8 for 81 and pass 50 in the Championship this season.
Although an afternoon downpour threatened to derail Warwickshire's success, leaving them with just 10 overs to chase 58, Rob Yates and Ed Barnard guided their side home with nine balls to spare.
Middlesex began the day 98 runs in arrears and Barnard immediately sent a couple of deliveries whizzing just past Robson's outside edge before the opener steered him through point for four.
However, Jack Davies soon perished to a rash stroke, having failed to increase his overnight score of 10 when he swatted a loose delivery from Miles into the hands of backward square leg.
The seamer also claimed the scalp of Joe Cracknell, who had just struck him for two boundaries but was lured into a trap next ball, miscuing the pull as Miles switched to around the wicket and tempted him with a short one.
Three down and 74 short of making Warwickshire bat again, the home side urgently needed a partnership and Higgins settled down to build one of 85 with Robson as the pair whittled down the deficit.
Two overs of offspin from Yates helped them to do that, disappearing for 20 as Higgins fished the reverse-sweep out of his locker and Middlesex went to lunch just 13 behind their opponents.
A stray leg-side ball from Miles that went for two byes took the batting side into positive territory and, in the next over, Higgins reached his half-century with a sweet straight drive off Barnard for four.
But the bowler quickly responded by breaching Higgins' defence to hit his off stump - just as he had done in the first innings - and reignited Warwickshire's prospects of pressing for victory, with the new ball on the horizon.
Those were strengthened further still as Danny Briggs had John Simpson caught at short leg before Hannon-Dalby and Chris Rushworth took joint ownership of the new ball, picking up a wicket apiece to plunge Middlesex deeper into trouble at 234 for 7.
Despite that pressure, Robson maintained his focus to progress to three figures from 251 balls, squirting Rushworth for a leg-side single, while Tom Helm dug in to deny Warwickshire further success prior to tea.
Having survived more than half an hour, Helm was undone by one from Hannon-Dalby that kept low and the same bowler eventually brought Ethan Bamber's dogged resistance to an end by finding the edge of his bat.
With the sky darkening, Warwickshire had to revert to spin and the second ball of Briggs' first over was enough to fox Tim Murtagh - who registered a duck in his final innings at Lord's - and leave the visitors with an apparent 25 overs to chase their modest target.
As Warwickshire's top-order batters sprinted towards the pavilion, though, the heavens opened and the resulting delay reduced their allocation of overs by 60 per cent when play resumed an hour later.
Alex Davies moved up to open and carted Murtagh into the grandstand for six before the bowler trapped him lbw - and a superb reaction by Simpson to stump Dan Mousley earned the 42-year-old his eighth wicket of the match.
But there was to be no fairytale finish for Murtagh, with Barnard clubbing Jayant Yadav over the top and running three to secure Warwickshire's victory.
