Light Blues midfielder Steven Whittaker was sent off by referee Calum Murray in the 35th minute after picking up his second booking for a foul on Emilio Izaguirre and consequently an uphill task for the injury-ravaged visitors became almost impossible.
Wilson drove in three minutes after the break after his first shot was cleared off the line by the head of Ibrox defender Sasa Papac – who was stretchered off for his troubles to add to the Light Blues’ woes.
The game ended in some chaos.
Rangers defender Madjid Bougherra was sent off in injury time after picking up his second yellow and after the game, as the two benches clashed for the second time, the unruly El-Hadji Diouf, booked earlier, got another yellow card for approaching Murray and was dismissed.
Rangers manager Walter Smith was angered by the dismissals, stating: “With Steven Whittaker, I wouldn’t have argued with the second yellow card but the first one, I felt he was fouled prior to the challenge, so therefore it was harsh.
“Madjid Bougherra’s one, he quite clearly wins the ball. I think that one was a complete over-reaction from the referee in the circumstances.
“As far as the last one is concerned, I don’t know what happened. That was after the game was finished.”
Until recently, Wilson had failed to find the back of the net for Celtic but he has now netted three goals in six games.
He said: “It’s unbelievable and it’s about time. It’s something I’ve always wanted to do for Celtic and then three come along and none more important than that in my opinion.”
With victory Celtic booked a place in the quarter-final away to Inverness and will be firm favourites to win the tournament.
For all their possession the home side could not fashion a clear chance in the opening stages.
In the 28th minute Ki Sung-yueng was fouled by Whittaker, which resulted in a yellow card for the Rangers midfielder who was dismissed seven minutes later after picking up another caution for a reckless challenge on Emilio Izaguirre.
Diouf and Hoops boss Lennon then had a touchline confrontation which earned the Light Blues player a booking and which threatened to plunge the game in to further disorder.
Referee Calum Murray then spoke to Rangers assistant manager Ally McCoist and Lennon – a spat which would come to a head later.
When play resumed a mistake by Ibrox midfielder Maurice Edu helped Georgios Samaras go through against Allan McGregor — but the Rangers goalkeeper made a great block from the striker’s close-range shot.
There was another fracas between Hoops’ assistant Johan Mjallby and Kyle Bartley as the players made their way up the tunnel at the interval, with Diouf involved again.
When Wilson scored three minutes after the break it put the home side firmly in the driving seat.
Izaguirre’s deep cross from the left found his fellow full-back at the far side of the box and his first shot was headed off the line by Papac – but the ball rebounded back to the former Dundee United player whose second effort found the target.
Papac failed to recover and was carried off on a stretcher, replaced by Gregg Wylde.
The game became increasingly antagonistic and Bougherra was cautioned for a foul on Gary Hooper which left the Celtic striker requiring treatment.
Deep into injury time Bougherra was dismissed after fouling commons – and there was more mayhem to come.
After the final whistle Lennon and McCoist had to be separated before Diouf received a second yellow and a subsequent red after approaching referee Murray.
Zaluska, Wilson, Majstorovic, Mulgrew, Izaguirre, Brown, Ki, Kayal, Commons, Hooper, Samaras.
McGregor, Foster, Weir, Bougherra, Papac (Wylde 51), Bartley, Whittaker, Edu, Davis, Fleck (Hutton 46), Diouf.
Referee: Calum Murray (Scotland).