Conor Chaplin's first-half header made it seven points from nine in their past three away games as Pompey prevailed at Cambridge for the third season in a row.
He nodded in Christian Burgess's ball into the box and Pompey worked hard to hold what they had - even after Amine Linganzi was sent off midway through the second half.
The points left the Blues still fifth in the table but only three points off the top three.
Pompey had Matt Clarke back in defence alongside Burgess in the only change from last week's line-up and it was a case of defences on top in the opening 20 minutes as neither side created much.
But it was the Blues who went in front on 24 minutes when Burgess broke away down the right and crossed for Chaplin, who had moved into space between two defenders to head past home keeper Will Norris.
A challenge by Burgess on Uche Ikpeazu had the home side and fans baying for a penalty but the referee was having none of it and booked James Dunne for his protests.
Kyle Bennett and Enda Stevens both tested Norris and there was little threat to Pompey's lead before the break.
The highlight of the opening part of the second half - in fact one of the more memorable points of the day - was a minute's applause nicely observed by home and away fans and Cook and his Pompey staff in the 53rd minute for Blues fan Gary Martin, who would have been 53 and watching his team today but was killed in a road accident in Portsmouth on Wednesday.
Ben Williamson missed a decent one-on-one chance for Cambridge and the home side got a boost when Linganzi was shown a straight red card for a lunge on Conor Newton that looked bad although didn't make a lot of contact.
Pompey had the best part of 30 minutes to hold out - but did so with great determination and backs-to-the-wall defending.
Danny Rose and Noel Hunt came on in place of Chaplin and Bennett as Pompey tried to shore things up and slow the game down and late on Gary Roberts was booked for a slow exit when he was replaced by Tom Davies.
Cambridge had plenty of pressure but few actual chances but Piero Mingoia and Dunne both tried their luck to no avail.
Pompey now have FA Cup action to focus on before their next league game and will be without Linganzi and Michael Doyle - who picked up his fifth booking of the season here - when Wycombe visit next Saturday.
After the game Cook praised the whole team for the way they saw out the game with a clean sheet, something they have been working hard on in training.
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