Hampshire 137 for 4 (Rossouw 60) beat Middlesex 136 (Eskinazi 43, Abbott 3-26) by six wickets
Hampshire stifled a vociferous 20,000 crowd at Lord's by cruising to a comfortable six wicket NatWest T20 Blast win with 15 balls to spare against weakened south group rivals Middlesex.
In pursuit of a modest Middlesex total of 136 all out, Hampshire cantered to their fifth win in 10 starts courtesy of an excellent 60 with six fours and a six by opening batsman Rilee Rossouw that cemented his side's place in the qualifying places.
Hampered by the loss of Dawid Malan, Toby Roland-Jones and Steve Finn on England duty, injuries to Paul Stirling and James Fuller, coupled with the absence of overseas stars Brendon McCullum and Tim Southee, Middlesex underperformed in every department to crash to the fifth defeat of a disjointed qualifying campaign.
Man-of-the match Roussouw was delighted after scoring his first 50 at headquarters. "The pitch was initially a little slower than we thought," said the South African. "It slowed up a little after their innings so we had to adjust."
Roussouw was struck on the head by a quick bouncer from young Middlesex quick Tom Barber but shook off the blow to lead Hampshire to victory.
"My head's fine but my face is the money-maker and that's good, so I'm very happy about that too," he said.
"To score runs here at Lord's is something that I've dreamt about since I was a little boy starting out paying cricket and I've got no words other than I'm very happy."
Hampshire's run chase started briskly when James Vince pulled the fifth ball of their reply from Barber for six into the Mound Stand.
Rossouw shook off his blow on the helmet by pulling Harry Podmore for another Mound Stand maximum. Three balls later, Vince danced down the pitch to lash another six over long-off off the same bowler.
Helm hit back by brushing Vince's off bail out of its slot with a slower ball that sent Hampshire's skipper packing for 20 but, having taken good advantage of the Powerplay fielding restrictions, the visitors were already well ahead of the chase on 56 for 1 after six overs.
With the field scattered, Tom Alsop (10) risked a second run to Ryan Higgins in the deep to be run out by a yard, then, with 79 on the board, George Bailey also departed to a run out after jogging a risky single to Stevie Eskinazi at square leg.
Rossouw posted the only half-century of the night and the 15th of his T20 career from 39 balls. With only 14 needed Rossouw departed by top-edging an attempted paddle to long leg, but his innings had ensured Hampshire's comfortable win.
Batting first after winning the toss Middlesex openers Nick Gubbins and Eskinazi made a scrappy start with more shots coming off the edge rather than the middle of their bats.
Gubbins appeared to struggle for timing and his stay proved a short one when he miscued an attempted lofted drive against Chris Wood to mid-on.
John Simpson marched in to increase the urgency out in the middle with a few sharp singles but Middlesex could only muster 42 by the end of the Powerplay.
The hosts targeted young Hampshire leg-spinner Mason Crane after his introduction from the Pavilion End with 16 coming from the over including a slog sweep for six by Eskinazi.
The hosts had 65 on the board when Hampshire seamer Tom Holland marked his debut with a wicket with his fourth ball when Simpson pulled a short one straight to Bailey at long leg.
Crane settled down in his second over to peg back Eskinazi's off stump after the right-hander swept across the line of a top-spinner to go for 43 from 27 balls.
Experienced fourth-wicket partners Eoin Morgan and Adam Voges attempted to improve their side's sedate tempo as Morgan latched onto successive short deliveries from Holland to hit the ropes at midwicket.
In his 230th appearance in the short form Morgan moved past 5,000 T20 career runs helping Middlesex to reach 83 for three at the mid-point of their innings. The Irishman reached 22 from 14 balls when, in aiming to late cut, he dragged slower ball from Wood onto his stumps to leave the hosts in a pickle on 95 for 4 as Wood finished with 2 for 26.
Gareth Berg returned to bamboozle James Franklin with a slower ball out the back of the hand that the Kiwi all-rounder obligingly skied to Alsop at deep mid-wicket.
In the next over Voges called for a suicidal single to Rossouw at backward point to be run out after losing the race against the throw by a couple of yards at the non-striker's end.
Hampshire's domination continued when Wood leapt to snaffle an incredible one-handed overhead catch at extra cover off a smeared drive by Ryan Higgins.
Nathan Sowter was caught off a miscued pull against Kyle Abbott, who then yorked Harry Podmore first ball to complete his excellent stint with 3 for 26.
Berg polished off the innings by bowling Barber with a full inswinger as Middlesex succumbed for their second lowest total at Lord's with five deliveries of the innings still to be bowled.
Morgan, the disappointed Middlesex skipper, felt his side's batting performance had tailed off after a reasonable start. He said: "We started well enough, almost 90 off 11 isn't too bad, but then we lost three or four in quick succession and couldn't recover.
"I thought the bowlers went alright. Hampshire are a very experienced team and our first six overs weren't too bad, a couple of catches might have made things a little bit easier for us, but we dragged it back. The fight we showed in the field was good, but we certainly didn't get enough runs."