The Clarets looked in cruise control following Rodriguez’s simple opener and a stunning strike from McNeil.
But Paul Cook’s Championship side struck back through Joel Pilkington’s goal before half time – and earned a confidence-boosting share of the spoils through Joe Gelhardt’s smart low effort after the break.
It was another strong side for the final pre-season trip of the season, with Ben Mee operating at centre back after missing last weekend’s double header.
And the Clarets had the perfect start in the fifth minute with a delightful opener.
Ashley Barnes spun onto a precise ball infield from Ashley Westwood and slid a perfect through ball to send Johann Berg Gudmundsson clear.
The Icelandic wide man could have gone for goal, but spotted Rodriguez unmarked on the penalty spot and slid the ball perfectly into the striker’s path for a simple tap-in.
Five minutes later, the lead was doubled in fine style.
Again, Gudmundsson and Barnes were the architects and when the latter laid the ball off, McNeil fired a terrific first-time effort into the bottom right hand corner from outside the area.
Pilkington fired over from just inside the areas as Wigan carved out their first opening of the game midway through the opening half.
The Blackburn-born youngster then forced a fine save from Tom Heaton with a rising drive on the half hour, and almost immediately halved the deficit by turning home a low cross from inside the six-yard box.
But as half time approached the chances continued to come for Burnley and, after Gudmundsson beat the offside trap to fire wide, Barnes forced a fingertip save from David Marshall after plucking a long ball out of the sky and going for the bottom corner.
Wigan spurned a golden chance to level the scores shortly after the restart when Lopes fire a ball across the six-yard box and the in-rushing Windass completely fluffed his lines.
And on the hour mark, Burnley were grateful to Heaton for a fine save from Michael Jacobs, after the Latics’ showed neat footwork to create the opening.
A flurry of Clarets substitutions followed, but it was still the hosts’ posing most of the questions.
And the equaliser duly arrived midway through the half as substitute Gelhardt smashed home from 12 yards.
Burnley responded and Wood, so prolific in front of goal throughout pre-season, poked his effort wide after a terrific threaded through ball from substitute Jeff Hendrick.
But neither side could eek out the winner as the Clarets’ thoughts turned towards two Turf Moor friendlies in the coming week, ahead of the big kick off.
BURNLEY: Heaton, Lowton (Bardsley 61), Tarkowski, Mee (Long 61), Taylor (Pieters 71), Gudmundsson, Cork, Westwood (Hendrick 71), McNeil (Lennon 71), Rodriguez (Vydra 80), Barnes (Wood 61).
Subs: Hart, Younger.
WIGAN (starting): Marshall, Dunkley, Kipre, Evans, McLeod, Robinson, Lopes, Pilkington, Jacobs, Windass, Garner.
Subs: Jones, Fox, Naismith, Massey, Roberts, Weir, Byrne, Gelhardt, Lang.