Jones' win sets up a last 32 clash against Roland Scholten next Thursday, after the Dutchman had knocked out Jamie Caven in the opening match of the competition earlier on Thursday.
MacKenzie, who defeated Paul Barham in their preliminary round game earlier in the evening, started well and established a 2-1 lead in the first set.
Jones held throw for a second time to take the fourth leg and hit double five with his last dart in the deciding leg to take edge ahead.
The Wolverhampton star drew confidence from taking the opening set as he hit 180s in each of the first two legs of set two to build a 2-0 lead.
Jones, who reached the semi-finals of this tournament back in 2006, took the set without reply as he converted a 75 finish to confirm a two-set cushion.
MacKenzie began the third set by hitting double top to win the first leg and then broke throw in the next by landing double ten.
Jones won the third leg against the darts with an 81 finish but MacKenzie took the fourth by hitting double ten once again to get back into the game.
MacKenzie capitalised on missed darts at doubles from Jones to win the first leg of set four, but the 15th seed recovered to take the second with a two-dart 68 finish, after MacKenzie missed the bullseye for a 167 checkout.
Jones hit double top to win the next leg against the darts and then closed out the game by landing double 16 at the first attempt.
"There were some patches of being pretty good there and it's great to be through," said Jones. "I know I hit a few 180s but it was a bit frustrating that I struggled to score well outside of that.
"Scott played really well and was more consistent than I expected, and if it had gone to a deciding set he'd have probably beaten me, so I'm pleased to get it over with."
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