This Alternate History is actually one of the easier ones to achieve.
Just prior to the 1988 debate there was a real movement within the top levels of the Liberal Party to replace John Turner with Jean Chretien. The executive had the power to do so, and were debating doing so. At the time the Liberals were near 20% in the polls, whereas polls suggested if Chretien were leader, the party would be doing better. Eventually the executive (rightly) decided that switching leaders mid election would be looked at poorly by voters. Luckily for the Liberals, the 1988 debate featured exchanges over Canada's participation in Free Trade with the United States, and the Liberals jumped from 20% to 45% literally overnight. The party could not maintain this position, and dropped back to second, finishing the election as the Official Opposition.
The NDP meanwhile had been doing very well in the polls, actually polling in first for part of 1987. This was important. The last time the NDP, or any of it's predecessor parties had polled in or near first was in 1943 when the CCF managed a first placed position in a Gallup poll. During 1987 many polls confirmed the NDP's position in first. The only other time the NDP managed multiple first place results in polls was in the 2011-2015 period.
1988 was the first real chance the NDP had to finish in second, and had Turner's debate performance not been so strong, they may well have done so. Regardless, when facing off against Chretien, we could have seen the following:
Chretien actually loses his own riding to the NDP. Not only did the NDP have a strong candidate here, but this is realistic given the expected backlash against swapping leaders. This keeps the Tories in government, but allows the NDP to form a strong official opposition of a bit less than 80 seats, while the Liberals are down closer to 30.
With Broadbent, a moderate, as NDP leader, this would likely have meant we'd see an NDP government in 1993; however I will save multiple-election Alternate History posts for later on.