Going way back:
1. Wish You Were Here (saved by the title song being a big Eddie Fisher hit and that the show had a swimming pool on stage);
2. Kismet (a newspaper strike was going on at the time that it opened, so the generally tepid reviews had no effect on the outcome);
3. Fanny (David Merrick showcasing); and
4. Pippin (first extensive television commercial).
In general, the NYT has an aversion to anything written by Andrew Lloyd Webber or Steven Schwartz and their megahits have withstood the NYT's barbs. Also, NYT is generally disinclined to favor the Disney products (as I recall, even Lion King didn't get undiluted praise).
BroadwayEd