The Bianconeri were stunned by Manchester United in Turin during their last group game but sealed their place in the last 16 with one game to spare on Tuesday, with Group H top spot now up for grabs on matchday six.
In a game of few chances, Mandzukic scored a tap-in in the second half after Cristiano Ronaldo had worked space to steer a cross to the Croatian striker.
United's last-gasp win over Young Boys means Valencia are out, with no way of reaching the last 16 even if they beat Mourinho's side at home in their final group game.
Juventus had been awarded two penalties in the reverse fixture with Valencia but Miralem Pjanic, the scorer of both of those spot-kicks, was denied another in the first half when he claimed he was pulled back by Geoffrey Kondogbia.
The Bianconeri dominated possession but struggled to conjure up chances and Joao Cancelo's outside-of-the-foot effort that went wide was as close as they came to a first-half goal.
It was Valencia who almost took the lead on the stroke of half-time, but Wojciech Sczcesny's brilliant one-hand save repelled Mouctar Diakhaby's header from a corner.
Juventus continued to look short of ideas until Ronaldo's moment of magic just before the hour mark.
The Portugal forward's stepover fooled Gabriel and gave him enough space to steer across a ball that Mandzukic turned home from close range.
Valencia thought they had hit straight back when Diakhaby got a touch to Dani Parejo's near-post free-kick.
However, the ball had clearly struck the defender's outstretched arm and rather than being credited with an equaliser, Diakhaby was punished with a yellow card from referee Willie Collum.
Neto denied Paulo Dybala, Ronaldo and Mandzukic a second Juve goal, but Valencia never looked like getting an equaliser at the other end as they exited the competition.
What does it mean? Juve through, but top spot not guaranteed
With Ronaldo now in their ranks, Juventus are considered one of the favourites for this competition and can now look forward to being in the last 16. However, United's late winner means they are not yet through as group winners, with Juve holding a two-point advantage with one game to go. The Italians must win their last game to be certain of sealing top spot.
Ronaldo exacts a measure of revenge
Ronaldo was controversially sent off against Valencia in the first meeting between the two, but he made a more positive contribution here with some fine skill to tee up Mandzukic for the winner. He also had eight shots on goal in a lively performance.
Valencia's tactics come back to haunt them
Valencia lacked attacking intent even after falling behind, registering only one attempt on target in the whole match. That may not have looked as costly when it was 0-0 at Old Trafford, but Marcelino's side went out with a whimper as soon as Marouane Fellaini struck in Manchester.
Key Opta Facts:
- Juventus have made it past the first group stage in 12 of their last 14 Champions League campaigns.
- They have kept a clean sheet in six of their last seven Champions League group games.
- Valencia have now failed to get past the group stages in three of their last four Champions League appearances.
- Ronaldo was on the winning side for the 100th time in the Champions League (157th game) – the first player to reach this milestone in the competition.
- Mandzukic has scored at least once in all seven of his previous Champions League campaigns, netting 21 times in total.
Valencia, who host United next month, do at least have the consolation prize of Europa League football in the new year, and Juventus round off their campaign at Young Boys eyeing first place. Domestically, Juve have a trip to Fiorentina on Saturday, while Valencia will hope to move into LaLiga's top half when they visit Real Madrid.