After heavy back-to-back losses to co-hosts Australia and New Zealand, England was under intense pressure in its Pool A match against Scotland at Christchurch on Monday.
Scotland had never beaten England in a one-day cricket international, but was confident after giving New Zealand a scare and had no hesitation in sending the English in to bat after winning the toss.
Moeen Ali came to the fore, scoring 128 and sharing a 172-run opening stand with Ian Bell, who scored 54, to set England on course for a big total of 303-8.
He picked up two wickets, and Steve Finn recovered from the battering he took against New Zealand to take 3-26, as England bowled Scotland out of 184 in 42.2 overs to secure a 119-run victory.
"I don't think there was ever a state of panic," said Morgan, who ended his own lean streak with the bat by scoring 46 from 42 deliveries. "Obviously we had two hard games and the fact that we didn't perform was most disappointing.
"But a win just puts things a little more at ease. It gives guys a little bit of confidence, even the guys who didn't perform today will benefit from guys who have had a little bit of success today."
England lost to Australia by 111 runs at Melbourne on the first day of the tournament, and slumped to an eight-wicket defeat to New Zealand last Friday after it was bundled out for 123 — the Kiwis needed only 12 overs to reach the victory target.
England had some wobbles against Scotland, with Ali, Gary Ballance (10) and Joe Root (1) all dismissed within the space of 10 balls, but Morgan held the lower order together with partnerships of 49 with James Taylor (17) and 45 with Jos Buttler (24) until he was dismissed in the last over.
Scotland started confidently in reply, with South African-born opener Kyle Coetzer making 71 runs and hitting 11 boundaries, but the loss of early wickets derailed the run chase.
"We're very disappointed," Scotland captain Preston Mommsen said. "We went into the halftime break pretty sure we were in with a shout. Unfortunately, with the bat we just couldn't get going. We're a better side than we showed today."
West Indies captain Jason Holder wants his team to live up to expectations when it plays Zimbabwe in Canberra on Tuesday, and knows Chris Gayle can have a big impact on that.
The West Indies bounced back from a demoralizing opening loss to Ireland to beat Pakistan by 150 runs on Saturday, and Holder is hoping to maintain the momentum.
"We still have full confidence in him, and it's very good to see that still he hasn't fired and we still gain 300 runs," Holder said. "I'm sure when his contribution comes, we'll get somewhere close to 400."
The West Indies won the first two Cricket World Cups, in 1975 and 1979, but haven't returned to the final since losing the championship match to India in 1983. It has been a long and painful decline for the Caribbean team, but 23-year-old Holder has a positive outlook on the future.
"It's early days for me in captaincy in terms of this West Indies team," said Holder, who took over in December, "but I think over time and once I can get my players to come together a lot to gel as one unit, I think we can be world-beaters."
Morgan was thrust into the England captaincy when Alastair Cook was dropped amid concerns over the team's force in the limited-overs arena. He's had to endure a lot of criticism in his short term at the helm, particularly for his run of low scores. The big win over Scotland helped England improve its net run rate, a statistic that could be important later when quarterfinal spots in each group are up determined. England's next game is against Sri Lanka in Wellington on Sunday.
"In your head I think you can be guilty of building up a tournament, convincing yourself you have to play your best throughout a tournament and hammer every side in order to win it, to gain confidence," he said. "The games I've watched haven't shown that at all — strong sides have been beaten. It's about getting points on the board."