Both had outstanding games at Stamford Bridge in what was an excellent team performance that won us a point at the home of the title favourites and it was Barnes who was voted the man of the match ahead of Mee with 61.5% of the vote against the 17.6% won by Mee.
Third and fourth places went to Mee's fellow defenders Jason Shackell and Kieran Trippier. Shackell took third place with 4.8% of the vote with Trippier coming fourth with a 3.9% share.
If Barnes beat Mee in the vote, they couldn't be separated in the player ratings. The pair came out on top with ratings of 8.53 each. Again Shackell was third with a rating of 8.21 with fourth place this time going to Michael Keane whose 8.16 out of 10 ensured all of the back four won points towards the Clarets Mad Player of the Year.
Barnes, of course, got the maximum ten points whilst there were eight points for Mee, four for Shackell and one each for Keane and Trippier.
Those points reduced Danny Ings' lead at the top to 23 points but we've now got Barnes pushing closest to Shackell having moved above George Boyd into third place. He is now only two points behind Shackell.
The next vote will get underway on Saturday within an hour of the final whistle of the home game against Swansea.
The result for the Chelsea game and the current player of the year table can be found below.
MAN OF THE MATCH
61.5% - Ashley Barnes
17.6% - Ben Mee
4.8% - Jason Shackell
3.9% - Kieran Trippier
3.6% - Michael Keane
2,4% - David Jones
2.1% - George Boyd
1.2% - Danny Ings & Michael Kightly
0.9% - Scott Arfield
0.6% - Tom Heaton
PLAYER RATINGS
8.53 - Ashley Barnes & Ben Mee
8.21 - Jason Shackell
8.16 - Michael Keane
7.84 - Kieran Trippier
7.74 - David Jones
7.37 - Scott Arfield
7.32 - Tom Heaton & Danny Ings
7.16 - George Boyd
7.11 - Michael Kightly
CLARETS MAD PLAYER OF THE YEAR
92: Danny Ings
69: Jason Shackell
67: Ashley Barnes
62: George Boyd
57: Scott Arfield
45: Kieran Trippier
36: Tom Heaton
34: Ben Mee
31: Lukas Jutkiewicz
30: David Jones
29: Michael Duff
26: Michael Keane
21: Dean Marney
17: Stephen Ward
14: Michael Kightly
10: Nathaniel Chalobah
6: Marvin Sordell
4: Sam Vokes
2: Ross Wallace
1: Matt Gilks & Matt Taylor