The competition holders are still waiting to hear the date for their return to Wembley for last season’s final.
But they produced a professional – and largely dominant performance – against their League Two opponents.
Both of the goals arrived in the space of a few first half seconds, with Harness displaying some precise finishing to secure all three group stage points.
Pompey handed debuts to full-back duo Cam Pring and Callum Johnson, who arrived from Bristol City and Accrington respectively over the summer.
They replaced Lee Brown and James Bolton, as Kenny Jackett made four changes from the side that won at Stevenage on penalties in the Carabao Cup 10 days earlier.
Craig MacGillivray came in for the injured Alex Bass between the sticks, while Paul Downing made way for Jack Whatmough.
The hosts dominated possession in the opening stages, although chances were hard to come by at both ends of the pitch.
It was the Blues who, unsurprisingly, had the first decent one following a fine bit of trickery down the left from Ronan Curtis.
He sent the ball into the centre and it bounced off both Harness and John Marquis before being grabbed by grateful keeper Shamal George.
It was proving to be a quiet evening for MacGillivray at the other end, although he had to deal with a simple angled effort from Miles Welch-Hayes.
Pompey were looking more likely to break the deadlock, although Gareth Evans could not bring Curtis’ pass under control and the ball flew harmlessly wide.
Referee Craig Hicks then got in Luke Gambin’s way during an attack from the home side and would undoubtedly have been relieved to see the move break down.
Curtis was looking a real threat for the Blues and following one mazy run, his placed shot was saved low down by George.
A goal seemed to be moving closer as the first half progressed and a corner was nodded over by Sean Raggett.
And the deadlock was broken on 37 minutes, with HARNESS collecting a pass from Curtis and firing in a shot that had too much power for George.
HARNESS then scored his second in as many minutes, racing onto a long ball over the top from Whatmough and clinically finding the net.
There was still time for Tom Naylor to go close before the break, with the skipper stealing possession and scuffing his effort just past the post.
Colchester United 0
Pompey continued to dominate following the restart and an Evans corner caused problems, while Curtis then fizzed a shot narrowly wide.
The latter soon had another opportunity after being fed by Harness and his stabbed attempt was saved by George.
It was pretty much one-way traffic and a teasing delivery from Harness had to be dealt with by Omar Sowunmi before Evans could pounce.
Evans should probably have strengthened the advantage following another fine cross from Pompey’s goal hero, but his header was too deft.
MacGillivray was called into action to deal with Ben Stevenson’s drive on 65 minutes, although it was regulation stuff for the Scottish stopper.
Harness then tried to complete his treble at the other end, but could not make a clean connection with Pring’s cross.
His hat-trick hopes were over soon after, as he was withdrawn with fellow winger Curtis, as Andy Cannon and Ryan Williams came on.
Marquis then had a shot saved by the feet of George before also being replaced, with Ellis Harrison given a cameo.
The game had started to drift by that point, but it burst back into life on 86 minutes following a poor Colchester back-pass.
Harrison could not quite get there in time to tuck away the loose ball and Cannon was also denied before Evans blazed over.
The hosts had already comfortably done enough, though, and saw out the remaining moments to seal the victory.
Pompey (4-2-3-1): MacGillivray; Johnson, Whatmough, Raggett, Pring; Naylor (c), Morris; Harness (Williams 77), Evans, Curtis (Cannon 77); Marquis (Harrison 82)
Goals: Harness 37, 38
Booked: Williams, Pring
Subs not used: Turnbull, Bolton, Brown, Close
Colchester (4-2-3-1): George; Welch-Hayes, Sowunmi, Eastman (c), Scarlett; Stevenson, Chilvers; Poku (Cowan-Hall 66), Gambin (Marshall-Miranda 78), Senior; Brown (Taylor-Crossdale 66)
Subs not used: Coulter, Bramall, Smith, Harriott
Referee: Craig Hicks