With five matches to play, Molde have 51 points, two more than Rosenborg Trondheim. Stromsgodset are third on 48 and Tromso fourth on 42.
Molde manager Solskjaer described the clash against Sandnes as "a parody of a match" and said the pitch was so waterlogged the game should not have gone ahead.
Asked if it should have been postponed, Solskjaer told Norway's TV2: "Yes, you could see that after two minutes."
Molde got off to a flying start when Mattias Mostrom fired home from 20 metres in the third minute.
The lead was doubled 20 minutes later when Jo Inge Berget sent Sandnes goalkeeper Aslak Falch the wrong way from the penalty spot after a foul in the box on Molde's American forward Joshua Gatt.
Molde seemed to cope better with the wet conditions and appeared to be heading for a comfortable victory, but Sandnes goals in the 83rd and 85th minutes rocked the defending champions.
Molde struck back immediately with defender Vegard Forren firing an 86th-minute free kick into the top corner.
Sandnes forced a series of corners in the dying minutes but could not find an equaliser.
"It was fantastic to get three points," former Manchester United forward Solskjaer said. "Maybe not completely deserved, but the most important thing is that we took them."
Rosenborg, the 2010 champions, kept up their challenge with a 1-0 win over Odd Grenland thanks to a second-half goal from a very tight angle by Swedish striker Rade Prica.
Third-placed Stromsgodset, who face Molde at home next, drew 1-1 away to Valerenga on Friday.
A late goal by Oscar Hiljemark fired Elfsborg to the top of the table in Sweden's Allsvenskan as Stockholm club AIK lost ground in the title race with a shock 1-0 defeat at home to Gefle.
Elfsborg, from the town of Boras 60 km east of Gothenburg, have 52 points, two ahead of Gothenburg side Hacken BK, this season's surprise package, with Malmo FF in third a point further back and AIK Stockholm fourth.
Lasse Nilsson missed a penalty for Elfsborg in the 85th minute before Hiljemark netted his second goal of the game to give Elfsborg a 2-1 win at bottom side GAIS who were relegated with four matches remaining.
GAIS have had a miserable season with financial difficulties off the pitch and poor performances on it with just 12 points from 26 games so far.
AIK, who qualified for the group stages of this year's Europa league, lost 1-0 as Jakob Orlov scored an injury-time winner for Gefle, leaving the Stockholm side on 47 points and all but out of the title race.
AIK invested heavily during the summer, bringing in Daniel Majstorovic and Mohammed Bangura from Celtic and striker Henok Goitom from Almeria, but they struggled to break down a resolute Gefle side.
All of the top four clubs play away in the next round and AIK appear to have the toughest task as they travel to historic rivals IFK Gothenburg looking to keep their slim hopes of a championship victory alive.
In the Greek Super League Olympiakos Piraeus made it six wins from as many matches on Sunday with a 1-0 home success against Asteras Tripolis to maintain top spot.
Under-pressure Panathinaikos coach Jesualdo Ferreira got some respite as his team recorded only their second win of the season, a 2-1 victory at Skoda Xanthi, to move up to eighth in the table.
Leonardo Jardim's league leaders had Jose Cholebas to thank as the Greece full back's first-half strike proved the difference at the Georgios Karaiskakis stadium in a closely contested match in which the off-colour Reds were fortunate to come away with maximum points.
The win kept the champions three points clear of second-placed Panionios, who ran out 2-1 winners at PAS Yiannina.
"It was the most difficult win for the team so far this season," said Jardim.
"We knew that after a tough match in the Champions League with Arsenal we would be facing a difficult opponent and the team was tired having played three matches in a week," added the Portuguese.
"But we got the win and that is the most important thing, rather than the performance."
Panathinaikos picked up their win courtesy of a virtuoso display from Greece forward Lazaros Christodoulopoulos.
After the Greens fell behind to Marko Markovski's seventh-minute strike, the 25-year-old scored twice in three minutes just before the half-hour with a couple of incisive runs through the Xanthi defence.
Panathinaikos have seven points from six matches.