Jose Nunez cancelled out Messi's early opener, but further goals from Sergio Aguero, Angel Di Maria and Messi again put Alejandro Sabella's Albicelestes firmly in control.
Roque Santa Cruz grabbed a second goal in the 86th minute, but Maxi Rodriguez swiftly restored the visitors' three-goal cushion in the final minute to ensure Argentina qualified for next year's tournament in Brazil in some style - and with two games to spare.
Barcelona forward Messi got the Argentinians off to the perfect start by converting a 12th-minute spot-kick after Aguero had been fouled by Paraguay goalkeeper Roberto Fernandez.
Paraguay equalised six minutes later when Nunez connected with a cross from the left - albeit with a little help from Argentina goalkeeper Sergio Romero, who failed to catch an easy ball.
The visitors restored their lead in the 31st minute through Manchester City forward Aguero, who produced a superb left-footed finish despite the close attention of two defenders.
Real Madrid's Di Maria made it 3-1 four minutes after the interval following a fine pass from Fernando Gago, and Messi despatched another spot-kick three minutes later to further widen the gap.
Santa Cruz reduced the deficit in the closing stages, but Maxi consolidated the win one minute from the end.
The triumph moved Argentina onto 29 points in the Conmebol qualifying zone - three above Colombia, who lost 2-0 against Uruguay in Montevideo earlier on Tuesday.
The United States and Costa Rica clinched their places at next summer's World Cup finals in Brazil on Tuesday - with two rounds of matches to spare in the CONCACAF qualifying zone.
Jurgen Klinsmann's USA enjoyed a 2-0 win over arch rivals Mexico in Columbus, while the Ticos progressed despite being held to a 1-1 draw in Jamaica - courtesy of the fact there was not a winner in the Honduras-Panama encounter.
Eddie Johnson capitalised on a mistake by Mexico goalkeeper Jesus Corona to put the Americans ahead against Mexico four minutes into the second half and, 11 minutes from time, Landon Donovan converted Mikkel Diskerud's cross to put the result beyond doubt.
Klinsmann's side could have stretched their advantage even further but captain Clint Dempsey sent a penalty wide in stoppage time.
In Kingston, Randall Brenes put Costa Rica ahead with a right-footed strike in the 73rd minute after a mix-up in the Jamaica defence.
Jermain Anderson put a slight dampener on the visiting fans' celebrations with a stoppage-time equaliser for the bottom-placed Reggae Boyz, but the point proved enough for Costa Rica to ensure their fourth World Cup appearance - following adventures in 1990, 2002 and 2006.
Saturday September 14
12:45 Man Utd v Crystal Palace
15:00 Aston Villa v Newcastle United
15:00 Fulham v West Brom
15:00 Hull City v Cardiff City
15:00 Stoke City v Manchester City
15:00 Sunderland v Arsenal
15:00 Tottenham v Norwich City
17:30 Everton v Chelsea
Sunday September 15
16:00 Southampton v West Ham United
Monday September 16
20:00 Swansea City v Liverpool
NEWCASTLE UTD RESULTS
NEWCASTLE 1 FULHAM 0 (Ben Arfa)
Krul, Debuchy, Yanga-Mbiwa, Coloccini, Santon, Ben Arfa, Sissoko, Anita 65' (Cabaye), Marveaux 74' (Remy), Shola Ameobi 65' (Gouffran), Cisse
Subs: Gosling, Elliot, Sammy Ameobi, Dummett
NEWCASTLE 0 WEST HAM 0
Krul, Debuchy, Yanga-Mbiwa, Coloccini, Santon, Ben Arfa, Sissoko, Anita, Marveaux 66' (Sammy Ameobi), Shola Ameobi, Cisse 72'
Subs: Gosling, Bigirimana, Elliot, Vuckic, Dummett
MAN CITY 4 NEWCASTLE 0
Krul, Debuchy, Coloccini, S Taylor, Yanga-Mbiwa, Sissoko, Tiote, Gouffran 45+4' (Dummett), Ben Arfa 65' (Sammy Ameobi), Gutierrez 44' (Anita), Cisse
Subs: Elliot, Marveaux, Shola Ameobi, Obertan
MORECAMBE 0 NEWCASTLE 2 (Shola Ameobi, Sammy Ameobi)
Elliot, Debuchy, Yanga-Mbiwa, Good, Dummett, Bigirimana, Gosling, Marveaux 88' (Sissoko), Vuckic 46' (Shola Ameobi), Sammy Ameobi, Gouffran 71' (Ben Arfa)
Subs: Santon, Anita, Alnwick, Streete
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NEWCASTLE UTD 1 FULHAM 0
1. Tim Krul
26. Mathieu Debuchy
13. Mapou Yanga-Mbiwa
2. Fabricio Coloccini
3. Davide Santon
10. Hatem Ben Arfa
7. Moussa Sissoko
8. Vurnon Anita 65'
22. Sylvain Marveaux 74'
23. Shola Ameobi 65'
9. Papiss Cisse
4. Yohan Cabaye 65'
11. Yoan Gouffran 65'
14. Loic Remy 74'
15. Dan Gosling
21. Rob Elliot
28. Sammy Ameobi
36. Paul Dummett
Hatem Ben Arfa ended Newcastle's wait for a Barclays Premier League goal after 411 minutes to hand Alan Pardew a precious victory over Fulham.
The France international produced a piece of individual magic four minutes from time to create half a yard of space and rifle a stunning left-foot shot past the helpless David Stockdale to claim a first league win of the season.
Until his last-gasp intervention, it looked like being another frustrating afternoon for Pardew and his players as chances came and went without the deadlock being broken.
Papiss Cisse saw a 78th-minute header come back off the crossbar and Yoan Gouffran, who passed up a glorious opportunity against West Ham last weekend, glanced a header harmlessly wide with the goal with his mercy after Yohan Cabaye had been introduced to a mixed reception as a second-half substitute.
But Ben Arfa's inspiration proved enough to send Newcastle into the international break with the win they craved, although with Cabaye's future unresolved and a desperate search for reinforcements ongoing.
Newcastle dominated for long periods as Fulham arrived prepared to soak up what pressure their hosts could muster and then hit them on the break.
However, the killer instinct which has deserted since the end of last season continued to be conspicuous by its absence as a series of openings, albeit few of them clear-cut, went begging.
Mathieu Debuchy and Cisse were both denied by Stockdale before the break, and the keeper did well to claim Ben Arfa's deflected 62nd-minute effort.
Pardew sent on loan signing Loic Remy, the only new face to arrive at St James' Park so far this summer, with 16 minutes remaining, and his arrival prompted a fresh assault on the Fulham goal, although ultimately to no avail.
And it might have been even worse for the 52-year-old when Adel Taarabt was presented with the ball by Fabricio Coloccini 15 yards out, although keeper Tim Krul, who had earlier clawed away Bryan Ruiz's goal-bound free-kick, saved once again.
NEWCASTLE UTD FIXTURES
Saturday September 14
15:00 Premier League
Aston Villa v Newcastle United
Saturday September 21
15:00 Premier League
Newcastle United v Hull City
Wednesday September 25
19:45 League Cup - 3rd Rnd
Newcastle United v Leeds United
Monday September 30
20:00 Premier League
Everton v Newcastle United
Saturday October 5
15:00 Premier League
Cardiff City v Newcastle United
Saturday October 19
12:45 Premier League
Newcastle United v Liverpool
Sunday October 27
13:30 Premier League
Sunderland v Newcastle United