The 18-year-old produced a composed finish in the 24th minute to add to Victor Wanyama's early headed opener. Charlie Mulgrew fired Celtic three ahead just after the break and Watt was on hand to make it 4-0 in the 64th minute. However, Ross Draper scored two late consolations.
The win came despite Celtic being forced into six changes following their Champions League win over Helsingborg on Tuesday. Thomas Rogne, Scott Brown, Georgios Samaras, Kris Commons, Beram Kayal and Joe Ledley all dropped out through injury, but Wanyama returned with Filip Twardzik alongside him in central midfield.
Mikael Lustig, Kelvin Wilson and Paddy McCourt were also handed starts as Lennon utilised his squad in their fourth consecutive away game following a Philadelphia friendly against Real Madrid, a draw against Ross County and the win in Sweden.
Inverness were without suspended midfielders Richie Foran and Owain Tudur Jones and a first game against Celtic proved the steepest of learning curves for the summer signings in their starting line-up - defenders David Raven, Simon King and Gary Warren plus midfielder Draper.
Celtic showed no signs of travel-weariness as they took the game by storm. Gary Hooper nutmegged King and had a driven shot parried by Ryan Esson and Celtic scored from the resulting fourth-minute corner. Adam Matthews drilled a corner on to the six-yard line and Wanyama rose above a crowd of bodies to head into the roof of the net.
Caley Thistle improved but they were caught on the break when Twardzik played the ball forward for Watt. The former Airdrie striker flicked the ball through King's legs, raced clear and guided the ball into the corner from 18 yards.
Celtic netted within three minutes of the restart following a free-kick 18 yards out on the left. Matthews rolled a square pass into the box and Mulgrew escaped Shane Sutherland's attentions to drill the ball into the bottom corner. Substitute Josh Meekings and Andrew Shinnie had shots straight at Forster before Celtic went four up in the 64th minute.
Emilio Izaguirre ran on to McCourt's flick before leaving Nick Ross in a heap and his back-post cross found Matthews in space. The Welshman could not get a clean shot in but he managed to steer the ball into the path of Watt, who steered the ball home from six yards.
Caley Thistle grabbed a consolation in the 82nd minute when Draper ran on to Shinnie's through ball and finished low inside the near post. Gavin Morrison soon wasted another good chance and Draper grabbed his second from close range after Forster had parried his initial effort following Doran's cross.
Source: PA
Source: PA