England trailed 6-3 at half-time but a second-half comeback saw Smith put in a lively display and cross under the posts from an inside pass from Shane Geraghty.
Scrum-half Joe Simpson popped up from the back of a scrum to give the Saxons some daylight as they led 20-12 but Argentina struck back through replacement Tomas Roan.
Varndell’s 10-metre dash for the line after grabbing the ball from a ruck put Saxons eight points clear in the 70th minute and Stephen Myler’s drop goal on the whistle cemented victory.
The England pack included Tigers prop Dan Cole, gaining his first Churchill Cup experience after making his Saxons debut this season against Portugal, and openside flanker Ben Woods at his third Churchill Cup.
England Saxons
15 Nick Abendanon (Bath)
14 Tom Varndell (Leicester Tigers)
13 Dominic Waldouck (London Wasps)
12 Shane Geraghty (London Irish)
11 Matt Smith (Leicester Tigers)
10 Danny Cipriani (London Wasps)
9 Joe Simpson (London Wasps)
1 David Flatman (Bath)
2 Rob Webber (London Wasps)
3 Dan Cole (Leicester Tigers)
4 Peter Short (Bath)
5 Stuart Hooper (Bath, captain)
6 Chris Jones (Sale Sharks)
7 Ben Woods (Leicester Tigers)
8 Luke Narraway (Gloucester)
Replacements
16 Tom Mercey (Saracens) for Cole 40min
17 Mark Lambert (Harlequins) for Flatman 68min
18 Neil Briggs (Sale Sharks)
19 Tom Guest (Harlequins) for Narraway 60min
20 Phil Dowson (Newcastle Falcons) for Short 40min
21 Micky Young (Newcastle Falcons) for Simpson 75min
22 Stephen Myler (Northampton Saints) for Cipriani 65min
Scorers:
Tries: Smith, Simpson, Varndell
Pens: Cipriani (2)
Cons: Cipriani (2)
Drop Goal: Myler
Argentina Jaguars: 15 Martin Rodriguez (Atletico de Rosario), 14 Tomas De Vedia (London Irish), 13 Matias Viazzo (Bourgoin), 12 Horascio Alberto San Martin (Tala RC), 11Francisco Jose Merello (Regatas de Bella Vista), 10 Ignacio Mieres (Perpignan), 9 Martin Landajo (CASI), 1 Juan Figallo (Jockey Club), 2 Agustin Creevy (Captain, San Luis), 3 Pedro Arocena Ledesma (Stade Francais), 4 Carlos Jose Caceres (Tucuman Lawn Tennis), 5 Mariano Galarza (Univeritario de La Plata), 6 Alejandro Tomas Campos (Pueyrredon), 7 Leonardo Senatore (GER), 8 Tomas Leonardi (SIC)
Replacements: Juan Francisco Gomez (Leeds), 17 Mauricio Raul Guidone (La Plata RC), 18 Tomas Roan (La Plata), 19 Agustin Guzman (Tucuman RC), 20 Francisco Cubelli (Belgrano Athletic), 21 Benjamin Urdapilleta (CUBA), 22 Lucas Bernado Oro (Universitario)
Scorers:
Tries: Roan
Pens: Rodriguez (5)
