Bayern Munich striker Lewandowski struck again in what has been a remarkable qualifying campaign as Poland recovered from throwing away a two-goal lead in Warsaw to secure a first trip to the World Cup finals since 2006.
"I was angry. We were leading 2-0 at home and then let them equalise for 2-all. We had to score that third goal to calm things down," said Lewandowski, who moved back ahead of Cristiano Ronaldo's 15-goal tally.
Krzysztof Maczynski and Kamil Grosicki struck early as Poland made a dream start, but Montenegro hit back through goals from Stefan Mugosa and Zarko Tomasevic to pull level with just seven minutes left.
Lewandowski restored Poland's advantage on 85 minutes before a late own goal from Filip Stojkovic sealed victory, although Denmark's 1-1 draw at home to Romania ultimately rendered the outcome irrelevant.
"Congratulations to all the players who were able to hold on until the end," said Poland coach Adam Nawalka. "The players have proved themselves in difficult moments, hence our qualification and it's in very good style."
The Danes needed to win in Copenhagen while hoping that Montenegro could upset Poland to finish top of Group E, but Ciprian Deac's late equaliser cancelled out a 60th-minute penalty from Christian Eriksen.
However, Denmark are at least assured of a place in next month's play-offs as one of the eight best runners-up from the nine qualifying groups.
Germany made it 10 wins from 10 in Group C after routing Azerbaijan 5-1 in Kaiserslautern to join Spain as the only nations in history to finish a European World Cup qualifying campaign with a perfect record.
Leon Goretzka's opening goal was negated by Ramil Sheydaev on 34 minutes, but Sandro Wagner and Antonio Ruediger scored after half-time before Goretzka notched his second and Emre Can completed the victory.
Germany scored a European qualifying record 43 goals on the road to Russia, emulating Spain who achieved perfection in qualifying ahead of their triumph at the 2010 tournament in South Africa.
"It will be hard to win the World Cup for a second time."
- Agony for Scotland -
Northern Ireland slid to a 1-0 defeat to Norway in Oslo after an own goal by Chris Brunt, but Michael O'Neill's men were already guaranteed a berth in the play-offs after earlier results.
Slovakia face an anxious wait to discover whether they will advance to the two-legged play-offs after finishing second behind England in Group F following a comfortable 3-0 win over Malta.
Adam Nemec grabbed a brace with Ondrej Duda adding a third in Trnava as Slovakia extended Scotland's 20-year exile from the finals of major tournaments.
Gordon Strachan's team arrived in Slovenia two points clear of Slovakia going into the final round of matches, but dropped to third after being held to a 2-2 draw in Ljubljana.
Leigh Griffiths stroked the visitors into a first-half lead, but Slovenia equalised and then went ahead as Roman Bezjak netted twice after coming on at the break.
Robert Snodgrass handed Scotland a lifeline with an 87th-minute equaliser, but it wasn't enough as Scotland finished level on 18 points with Slovakia but behind them on goal difference.
"I have never been in a dressing room as silent as that," said Strachan, who refused to be drawn on his future as Scotland manager.
"At this moment, I am the last person thinking about that."
England won 1-0 away to Lithuania to conclude an unbeaten campaign as Harry Kane scored a 27th-minute spot-kick won by Tottenham Hotspur team-mate Dele Alli.
The in-form Kane, whose stoppage-time winner against Slovenia on Thursday secured England's place in Russia, has now scored nine goals in his last five matches for both club and country.
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