Johnson's 38th-minute strike was the difference between the two sides until the 83rd minute, when Podence found the back of the net to level the scores.
The result has moved Forest onto 27 points, leaving them in 14th position in the Premier League table, one point and one position behind their opponents on the afternoon.
The first opportunity of the match arrived in the eighth minute when Johnson's pace took him past Max Kilman and into a dangerous area, but the Forest forward's effort was tipped over the crossbar by Jose Sa.
Wolves came close to making the breakthrough in the 26th minute when Matheus Nunes's cross, which was meant for Matheus Cunha, was flicked towards his own goal by Forest defender Moussa Niakhate, but the woodwork came to the home side's rescue with Keylor Navas beaten.
It was Forest that took the lead in the 38th minute of the contest, with Johnson finding the back of the net for the eighth time in the Premier League this season.
The 21-year-old was found by Danilo inside the Wolves box after smart work from Morgan Gibbs-White, and the attacker made no mistake, converting past Sa to open the scoring at the City Ground.
Emmanuel Dennis came close to doubling Forest's advantage late in the first period, but his over-head kick from a Felipe header missed the crossbar.
Wolves had a shout for a penalty in the 52nd minute when Adama Traore went down inside the box under pressure from Felipe, but the referee was not interested and VAR agreed.
Sa made a smart save to keep out a strike by Dennis in the 63rd minute, before Johnson fired wide from the rebound, with just the one goal separating the two sides heading towards the final 25 minutes.
The next half-chance of the match came for Wolves in the 68th minute, but Kilman's attempt never threatened to trouble Navas, with his effort flying wide of the post.
The visitors did manage to find a leveller in the 83rd minute, though, with Podence picking out the far corner of the net after Pedro Neto had a strike blocked on the edge of the box.
Tempers boiled over in the latter stages, and there was a VAR check for a possible red card on Podence, but both teams finished with 11 men, as the points were shared at the conclusion of the contest.
Forest have another huge game on Tuesday evening away to Leeds United, while Wolves will be bidding to return to winning ways when they welcome Chelsea to Molineux next weekend.