Ward was two sets down against John Isner but was always close to the American number one and he dug out a sensational fightback to win 6-7 (4/7) 5-7 6-3 7-6 (7/3) 15-13.
Isner, the man who triumphed in the longest tennis match in history, saved five match points but Ward finally prevailed after the world number 20 hit a backhand into the net from close range.
Andy Murray had earlier thrilled his home crowd with a lightning start to the World Group first-round encounter, taking the first two sets inside 46 minutes against Donald Young.
Young fought back admirably after looking out of his depth but Murray ultimately cruised home 6-1 6-1 4-6 6-2.
Ward and Isner were evenly matched throughout and the Briton had been 4-2 up in the first-set tie-break, but his opponent got a stroke of fortune with a net shot and never looked back.
The American edged further ahead after finally breaking in the 11th game of the second set when Ward was wide with a backhand, finishing the set off with a trademark power serve.
The third set started in a similar fashion with serves being held but Ward brought the house down with two cross-court shots to break in the sixth game, before going on to seal the set with an ace.
The pair remained neck and neck throughout the fourth set but Ward, who is ranked 111 in the world, quickly took control of the tie-break and won 7-3.
Isner prevailed 70-68 final-set triumph against Nicolas Mahut at Wimbledon in 2010, a match that lasted 11 hours and five minutes, and he looked like hanging on in Glasgow but Ward showed no sign of wilting and eventually prevailed to the delight of a vocal home crowd.
Murray admitted he had been charged up by the atmosphere in front of more than 7,500 fans.
The world number five set the tone for proceedings as he dropped just one point in the opening two games and Young struggled to return throughout the first two sets.
The American did not even register a point during four consecutive games that spanned the first and second sets, but he rediscovered some resilience at the start of the third set, hanging on to his serve during a series of rallies.
The underdog continued to struggle on Murray’s serve until the 10th game, when two long forehands from the Scot handed Young the set.
The world number 47 looked a different player as he buzzed around the indoor court but Murray’s class told.
“When you play in an indoor arena everything feels so much louder and the noise stays in,” he said.
“It was very nice and I used that energy and emotion very well at the beginning of the match.
“I played extremely well, I would say for the whole match. I maybe had a slight lull in intensity but I couldn’t maintain the intensity I had in the first couple of sets for the whole match.”
When asked if he thought Young had been intimidated by the atmosphere, Murray said: “He didn’t start the match well but I made one unforced error in the first two sets. So, I can’t say it was down to his bad play why I was in that position. I’m going to praise myself today.
“One unforced error in two sets is going to get you a 6-1 6-1 lead. If he was intimidated, I think I also played my part in doing that.”