Tade fired into the top corner from long range midway through the second half as Motherwell again failed to win in the SPL at Fir Park.
The home side started well but ran out of ideas in the second half as they slipped out of the top three for the first time this season.
The victory moved Inverness nine points clear of bottom club Dunfermline and will prompt hopes they can push up towards the top six.
Motherwell, with Steve Jennings on the bench after a hamstring problem, have not picked up three points at home since September, but they began at a high tempo with Omar Daley playing up front alongside Michael Higdon in an attacking formation.
Inverness brought in Greg Tansey and Nick Ross to their midfield for the suspended Richie Foran and David Davis, who returned to Wolves after his loan spell, and they quelled the early pressure.
Inverness centre-backs Roman Golobart and Kenny Gillet were excellent throughout and, apart from some hopeful penalty appeals, their first concern came when Ryan Esson came out to block from Daley at his near post after Murphy had played the Jamaican down the left wing.
The visitors soon survived a scramble when Esson could not punch Tom Hateley's corner far from his crowded goalmouth but Tade did well to block from Higdon eight yards out.
Inverness created a good chance in the 29th minute when Lee Cox set up a counter attack and Tade played the ball through for Billy McKay, but the striker missed the target with his angled drive from 20 yards.
Motherwell had an equally dangerous opening a minute later when Murphy helped the ball on for Daley after Higdon had won a long ball. Daley worked an opening only for Thomas Piermayr to recover with a challenge that forced the Motherwell player to shoot over from 15 yards.
Daley returned the favour for Murphy with a return ball that saw the Motherwell winger race clear down the left wing. Murphy took the ball round Esson at pace but Piermayr got back to clear with the forward claiming in vain that he had been brought down.
Darren Randolph saved low drives from Tade and Tansey in the final stages of the half and Jonny Hayes forced another save from Randolph following a direct run seconds after the restart.
Esson soon held Lasley's powerful drive at the second attempt and the Inverness goalkeeper had to scramble to punch away Hateley's corner, which was heading straight in.
But the visitors were generally looking comfortable and McKay played Tade in the left channel, however Randolph narrowed the angle well and blocked from close range.
Tade soon converted a much more difficult chance in the 67th minute, picking up a loose ball and quickly unleashing a powerful strike into the top corner from 22 yards to leave Randolph with no chance.
Motherwell brought on Chris Humphrey and Henrik Ojamaa with the latter initially livening up their forward play. Inverness responded by bringing on defender Steve Williams, who arrived on loan from Bradford in midweek, for Ross.
Ojamaa got in behind the new five-man defence but his cutback just evaded Higdon and Esson later got to Higdon's flick-on just before Humphrey.
Jennings came on with four minutes left but Inverness brought on another defender, David Proctor, and comfortably held out.