The home side took the lead through Lawrence Shankland, with the Scotland striker then missing a penalty before teenager Archie Meekison doubled the Tangerines' advantage before the break.
The Steelmen pulled a goal back in the second half through Christopher Long before snatching a dramatic draw deep into stoppage time through Devante Cole.
Motherwell have now only lost once in 11 games and Alexander was delighted with the way his players kept battling to the end.
He said: "The result wasn't going our way but it was an open game and both teams were trying to attack in numbers.
"They were more clinical than us but we had as many chances as they had to score.
"I just told the players at half-time that we could win it and they had to believe they would take the opportunities – they just had to take their chances when they came."
Alexander added: "That was the second time we have come back from 2-0 down against Dundee United and Hibs in the last few weeks and the energy in the team is excellent.
"You could see how fresh we were at the end to try and get that winner and it has paid dividends the way the lads have trained.
"We have had some good results and we want to finish on a high against Ross County this weekend.
"You don't come from 2-0 down twice in the space of a month without good character and a bit of spirit about you."
United boss Micky Mellon was disappointed to miss out on taking all three points but was still full of praise for the youngsters who had seized their chance against Motherwell.
He said: "The future of this club is trying to organically develop our young players into winning players.
"I see that as the way forward. Young Archie is a terrific little player who has trained with us most of the season.
"It was about giving him an opportunity and I loved his enthusiasm. It was infectious.
"He scored an unbelievable goal and it was also a great performance from Logan Chalmers as well.
"It was a positive night but disappointing we didn't close it out. Part of our development going forward has to be seeing those types of games out and getting the result."