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Murray's dominant display on Centre Court made him the most successful British man in Grand Slam history as he surpassed Fred Perry's total of 106 matches won at the four majors.
The US Open champion will play Britain's James Ward or Lu Yen-Hsun of Taiwan in the next round.
"I thought he played some solid tennis and didn't give much away, but I just managed to get breakthroughs at the end of the first and second sets. Then I played better in the third and pulled away," Murray said.
"It's a good start. There are always nerves before the first match at a Grand Slam, especially here for me. I'm glad to get it out of the way and keep improving."
While Murray will be delighted to have recorded the 107th Grand Slam victory of his career, he has another more significant Perry achievement in his sights as he bids to become the first British male winner of the Wimbledon singles' title since Perry in 1936.
Murray has enjoyed a remarkable run since last year's tearful Wimbledon final defeat against Roger Federer, thrashing the Swiss great to win the gold medal at the London Olympics and then beating Novak Djokovic in the US Open final to finally claim his first Grand Slam title.
But Wimbledon remains the holy grail for Murray and, with that in mind, there was even better news for the Scot as French Open champion Rafael Nadal, who had been a potential semi-final opponent, crashed out in stunning fashion against Belgian Steve Darcis over on Court One.
"It's obviously surprising but that's sport," he said.
"Rafa's not played on the grass this year and not much last year either.
"If you are a little bit off and your opponent plays well you can be in trouble. That happens."
There was never any chance of Murray suffering the same fate as Nadal.
Murray had reached the final of the last three Grand Slams before the recent French Open, which he was forced to miss with a back injury, and now boasts a 12-match winning run on grass.
Becker may have the same surname as compatriot and former Wimbledon champion Boris Becker, but the similarities end there.
The 32-year-old, ranked 95, fought hard but was out-classed from the moment he gifted Murray the first break with a tame backhand in the fourth game.
Becker was handed a lifeline when the Scot produced a double-fault on break point in the seventh game.
Earlier in his career that might have triggered a Murray meltdown but he is a far more mature player now and hit back to take the set with a break at 5-4.
Murray was never truly rattled by the German and his clever groundstrokes eventually forced enough errors from Becker to break for a 5-3 lead that effectively sealed the second set.
That was the signal for Murray to step on the gas and he surged to the finish line, taking the third set in the kind of imperious fashion that sent a clear message to his rivals for title.
Results on the first day of Wimbledon (x denotes seeded player):Men's singles:
First round:
Steve Darcis (BEL) bt Rafael Nadal (ESP x5) 7-6 (7/4), 7-6 (10/8), 6-4
Lukasz Kubot (POL) bt Igor Andreev (RUS) 6-1, 7-5, 6-2
Stephane Robert (FRA) bt Alejandro Falla (COL) 6-3, 7-6 (7/5), 7-5
Benot Paire (FRA x25) bt Adrian Ungur (ROM) 6-4, 4-6, 6-3, 6-1
John Isner (USA x18) bt Evgeny Donskoy (RUS) 6-1, 7-6 (7/5), 7-6 (7/3)
Adrian Mannarino (FRA) bt Pablo Andjar (ESP) 6-1, 6-2, 6-3
Dustin Brown (GER) bt Guillermo Garca-Lpez (ESP) 6-3, 6-3, 6-3
Lleyton Hewitt (AUS) bt Stanislas Wawrinka (SUI x11) 6-4, 7-5, 6-3
Nicolas Almagro (ESP x15) bt Jurgen Zopp (EST) 6-4, 7-6 (7/2), 7-5
Guillaume Rufin (FRA) bt Marinko Matosevic (AUS) 6-1, 4-6, 6-4, 6-3
Radek Stepanek (CZE) bt Matt Reid (AUS) 6-2, 6-2, 6-4
Jerzy Janowicz (POL x24) bt Kyle Edmund (GBR) 6-2, 6-2, 6-4
Jurgen Melzer (AUT) bt Fabio Fognini (ITA x30) 6-7 (5/7), 7-5, 6-3, 6-2
Julian Reister (GER) bt Luks Rosol (CZE) 6-3, 4-6, 7-6 (7/5), 6-7 (4/7), 6-4
Sergiy Stakhovsky (UKR) bt Rogrio Dutra Silva (BRA) 6-4, 6-0, 6-4
Roger Federer (SUI x3) bt Victor Hanescu (ROM) 6-3, 6-2, 6-0
Jo-Wilfried Tsonga (FRA x6) bt David Goffin (BEL) 7-6 (7/4), 6-4, 6-3
Ernests Gulbis (LAT) bt Edouard Roger-Vasselin (FRA) 7-6 (7/1), 6-4, 7-5
Fernando Verdasco (ESP) bt Xavier Malisse (BEL) 6-7 (5/7), 6-1, 6-4, 6-3
Julien Benneteau (FRA x31) bt Tobias Kamke (GER) 6-4, 6-7 (5/7), 6-4, 6-2
Juan Monaco (ARG x22) bt Bastian Knittel (GER) 6-4, 6-2, 6-3
Rajeev Ram (USA) bt Luks Lacko (SVK) 7-5, 6-4, 6-7 (2/7), 6-2
Kenny De Schepper (FRA) bt Paolo Lorenzi (ITA) 7-6 (8/6), 6-4, 6-2
Marin Cilic (CRO x10) bt Marcos Baghdatis (CYP) 6-3, 6-4, 6-4
Viktor Troicki (SRB) bt Janko Tipsarevic (SRB x14) 6-3, 6-4, 7-6 (7/5)
Andrey Kuznetsov (RUS) bt Albert Montas (ESP) 6-3, 6-4, 3-6, 6-3
Vasek Pospisil (CAN) bt Marc Gicquel (FRA) 6-3, 6-2, 7-6 (7/3)
Mikhail Youzhny (RUS x20) bt Robin Haase (NED) 6-4, 7-5, 7-5
Tommy Robredo (ESP x32) bt Alex Bogomolov Jr. (RUS) 6-2, 6-2, 6-4
Nicolas Mahut (FRA) bt Jan Hjek (CZE) 6-2, 6-4, 6-3
Lu Yen-Hsun (TPE) bt James Ward (GBR) 6-7 (4/7), 6-4, 7-6 (13/11), 7-6 (7/4)
Andy Murray (GBR x2) bt Benjamin Becker (GER) 6-4, 6-3, 6-2
Women's singles:
First round:
Monica Puig (PUR) bt Sara Errani (ITA x5) 6-3, 6-2
Silvia Soler (ESP) bt Misaki Doi (JPN) 1-6, 6-4, 6-1
Lesya Tsurenko (UKR) bt Lara Arruabarrena (ESP) 6-1, 6-3
Eva Birnerov (CZE) bt Varvara Lepchenko (USA x26) 6-2, 4-6, 6-4
Sloane Stephens (USA x17) bt Jamie Hampton (USA) 6-3, 6-3
Andrea Petkovic (GER) bt Pauline Parmentier (FRA) 6-3, 6-2
Petra Cetkovsk (CZE) bt Donna Vekic (CRO) 6-3, 6-1
Caroline Wozniacki (DEN x9) bt Estrella Cabeza (ESP) 6-0, 6-2
Marion Bartoli (FRA x15) bt Elina Svitolina (UKR) 6-3, 7-5
Christina McHale (USA) bt Alexa Glatch (USA) 6-4, 6-4
Camila Giorgi (ITA) bt Samantha Murray (GBR) 6-3, 6-4
Sorana Cirstea (ROM x22) bt Stefanie Vgele (SUI) 7-5, 7-6 (7/3)
Lucie Safarova (CZE x27) bt Lauren Davis (USA) 6-4, 6-0
Karin Knapp (ITA) bt Lucie Hradeck (CZE) 6-3, 6-4
Michelle Larcher de Brito (POR) bt Melanie Oudin (USA) 7-6 (9/7), 1-6, 6-4
Maria Sharapova (RUS x3) bt Kristina Mladenovic (FRA) 7-6 (7/5), 6-3
Petra Kvitova (CZE x8) bt Coco Vandeweghe (USA) 6-1, 5-7, 6-4
Yaroslava Shvedova (KAZ) bt Kiki Bertens (NED) 6-4, 6-3
Garbie Muguruza (ESP) bt Anne Keothavong (GBR) 6-4, 6-0
Ekaterina Makarova (RUS x25) bt Johanna Larsson (SWE) 6-3, 6-3
Carla Surez (ESP x19) bt Lourdes Domnguez (ESP) 6-2, 6-2
Mirjana Lucic (CRO) bt Sofia Arvidsson (SWE) 6-1, 6-4
Eugnie Bouchard (CAN) bt Galina Voskoboeva (KAZ) 5-7, 7-6 (7/5), 6-4
Ana Ivanovic (SRB x12) bt Virginie Razzano (FRA) 7-6 (7/1), 6-0
Jelena Jankovic (SRB x16) bt Johanna Konta (GBR) 6-2, 7-5
Vesna Manasieva (SRB) bt Yanina Wickmayer (BEL) 3-6, 6-2, 6-4
Bojana Jovanovski (SRB) bt Ajla Tomljanovic (CRO) 3-6, 6-1, 9-7
Kirsten Flipkens (BEL x20) bt Yulia Putintseva (KAZ) 7-5, 6-4
Alize Cornet (FRA x29) bt Vania King (USA) 4-6, 6-3, 6-1
Su-Wei Hsieh (TPE) bt Tatjana Malek (GER) 6-1, 6-0
Flavia Pennetta (ITA) bt Elena Baltacha (GBR) 6-4, 6-1
Victoria Azarenka (BLR x2) bt Maria Joo Koehler (POR) 6-1, 6-2
